Chicken or egg, which one came first? This is a question even the scientists have to debate within their community.
Have you ever watched science-fiction shows and imagined what it would be like to travel to other worlds? What an exciting adventure that would be! We could travel to the Pleiades, take a trip around a black hole, or see the Pillars of Creation themselves. One can only imagine all the possibilities that may exist in our infinite universe.
The trouble is getting there. I believe the famous author Douglas Adams states it best when he wrote:
Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space. 
The space between stars is so large, it takes years, decades, centuries or much longer for even light to traverse through it. We just do not have the technology to achieve the necessary speeds to even visit our closest celestial neighbour Proxima Centauri, the closest star to our sun, lies an astonishing 40 trillion kilometres from us! Distances like those are difficult for us to even comprehend. There is nothing in our everyday lives that can ever compare.
Science-fiction tends to work around these issues by creating fictional technologies that can achieve speeds great enough to overcome these distances. Warp drives, hyper-drives, and jump drives are all common troupes of science-fiction, but surely these are all fictional, right? Well, it seems that the line between science-fiction and reality is beginning to get a little blurry.
There are currently several ideas in the scientific community that are attempting to tackle the science underlying these technologies. Most seem to centre around the ideas of Einstein and his theories of relativity. The ideas range from building highly efficient engines capable of accelerating indefinitely to warping the very fabric of space-time itself. These ideas are highly interesting and open up all kinds of speculation on what we can expect if these technologies come to fruition.
Let's say we have a vessel that is capable of accelerating indefinitely. One can assume that this vessel would theoretically be capable of accelerating to very near the speed of light (SOL). Travelling near the SOL brings with it all the strange things general and special relativity predict. In order to ensure safe and responsible science, some questions must be addressed:
What would it be like to observe this vessel from an external reference frame? What about a synchronized reference frame? What are the effects that this vessel will have on the space-time around it? What about the passengers on board? How will these effects affect the vessel's target destination?
Each of these questions leads to more questions--many of which are still up for scientific debate. There is, however, a fair amount of existing research that attempts to answer some of these questions.
To answer the first part of the question, we must understand a few things about relativity. First, the Theory of Special Relativity (ToSR) tells us that an object will gain mass as it approaches the speed of light. This is due to the ToSR concept of mass-energy equivalence, represented by the famous equation E=MC^2. In this equation, E is energy, m is the objects mass, and c is the SOL. An object travelling at relativistic speeds has an awful lot of energy. This energy appears in the form of kinetic energy. This energy is added to the objects mass giving the object a new type of mass that is known as relativistic mass. This mass, by definition, is greater than the objects normal (rest) mass. The added mass is more difficult to accelerate and requires more energy, which adds more mass, and the cycle continues. This mass-energy equivalence prevents an object from ever reaching SOL by acceleration alone.
This brings another problem. There are now two masses for an object which can use to figure out the amount of energy and object has. An observer from a frame of reference at rest relative to the moving object would calculate the objects energy using its relativistic mass. An observer from a synchronized frame of reference would use the objects rest mass to calculate its energy (the observer is synchronized with the object, so it appears at rest.). This shows that an object's energy can appear to be different for different observers.
ToSR also predicts dilation of space-time. We know that the closer to SOL an object becomes, the harder it is to accelerate. But what if a vessel traveling almost the SOL had a passenger, and that passenger decided to move toward the front of the vessel? Wouldn't the passenger's motion be added to the motion of the vessel making the passenger's speed relative to an outside observer appear faster than light? It turns out, that due to space dilation, this does not happen. Space itself will actually contract at these speeds making any distance traveled on board the relativistic vessel progressively smaller the faster it went. The passenger would also appear to moving slower in time, like a slow motion video. From the passenger's frame, time outside the vessel appears to move faster. This is how nature keeps the SOL constant from all reference frames.
From what we know about ToSR, we can speculate what might happen to space-time around a vessel that is travelling at relativistic speeds. We know from the Theory of General Relativity (ToGR) that energy (mass) curves space-time like a bowling ball on a trampoline. This curvature gives rise to what we call gravity. The relativistic mass of the vessel is greater than its rest mass and it is continually increasing the faster the vessel goes. This extra mass increases the curvature of space-time around the vessel. In fact, to an outside observer, through a combination of the red-shifting of the light waves, spacial dilation, and space-time warping, the vessel would resemble a black hole!
This increased space-time warping could potentially have bad effects on objects it passes nearby. The space-time stretching creates large tidal forces that can rip and shred anything that comes too close. This implies that if the vessel were to pass an object close enough to be within the radius of the space-time warping, the space around it would instantaneously stretch and tear apart whatever objects that were formerly occupying that space. The space-time warping is thought to be temporary, as natural objects such as black holes also have powerful tidal forces, and leave no lasting damage to the space-time they move through.
The passenger inside the vessel should be safe from these tidal forces. They exist in a kind of 'warp bubble' isolated from the rest of the universe. To explain why, a few things need to be understood. From their frame, they do not appear to be contracting into something resembling a black hole. This implies that what an outside observer sees is an illusion, because if an object is not a black hole in one frame of reference, it is not a black hole in any frame of reference. As for the tidal forces from the space-warping, the warping curves around the object's mass keeping the space inside the 'warp bubble' flat.
So what happens when the vessel arrives at its destination? Unfortunately, there is not much scientific literature that describes this scenario greatly. There is, however, a bit of study into a related concept—the Alcubierre drive. The Alcubierre drive is a theoretical engine that, using an extraordinary amount of energy and an undiscovered 'exotic matter', can warp space-time around it into a 'warp bubble.' This 'bubble' could then be accelerated to extreme velocities, potentially even faster than light! This is because the vessel that uses the drive never moves locally. It is the space around it that moves. There is no law preventing space itself from traveling faster than the SOL.
A recent study by Brendan McMonigal, Geraint F. Lewis, and Philip O'Byrne of the University of Sydney discovered what could happen when an Alcubierre drive stopped. They discovered that it is quite bad for whatever is in front of the vessel when the drive is shut off. As the vessel travels through space, the 'warp bubble' collides with all types of particles, but mainly it collides with photons. These photons become trapped in the warp field and, due to relativistic effects, cease to experience time in the normal sense. This 'time-stretching' allows their energy to increase as the photons become more and more blue-shifted due to the Doppler effect. The team then discovered that once the drive is turned off, the photons that were trapped are free again, but with all the added energy of being progressively blue-shifted as the vessel travelled. The photons' momentums propel them toward the direction they were travelling at sufficient energies to vaporize whatever is in front of the vessel when it stops. Additionally, since the vessel can theoretically travel indefinite distances, the energy of the photons can rise without limit and even carry enough energy to destroy a planet! This is of course still very theoretical, but it shows that if we intend to create these relativistic vessels, we need a means of shielding the vessel from all the particles and photons in will collide with. These are the kinds of problems we need to solve before any theoretical engine capable of these speeds can be built and used.
A different approach involves a technology much closer to the theoretical vessel we began with. Mr. David Huang of Blue Energy Australia based in Sydney who has been designing an engine called the Blue Energy Buoyancy Engine (BEBE) that would theoretically be capable of managing energy efficiently enough to achieve a constant acceleration. It may even be possible, through relativistic effects, to warp space through acceleration alone, circumventing the relativistic limits on speed. He believes this engine could be built using our current understandings of physics and engineering. The specific details of the BEBE are currently awaiting patent approval and cannot be discussed here.
The BEBE would be powered by another technology designed by Mr. Huang - the Blue Energy Thermal Engine (BETE). The BETE functions by converting thermal energy into mechanical energy. Mr. Huang believes this to be the most efficient means of powering the BEBE. Essentially, the BETE converts the thermal energy from a fuel source, such as nuclear fuel, and converts it to mechanical energy of thermal gas expansion into any other form of energy, which will be efficiently utilized by the BEBE, which then the BEBE create an anti-gravity effect. This anti-gravity effect can be harnessed and used similar to the propellant in a reactive engine. Assuming there is enough efficiency, the fuel on board would be able to last quite a long time for constant acceleration providing both high speeds and artificial gravity. What makes BEBE different from other type of reactive engine is that BEBE minimizes mass ejection to extremely low level while virtual anti-gravity effect is achieved mostly by fuel energy consumption at extremely high level. How efficient in Blue Energy innovation is still a mystery known by its inventor.
So, which technology will reign supreme? Should we approach relativistic travel by warping space to achieve high velocities or achieve high velocities to warp space? The Alcubierre drive is an example of achieving relativistic speeds by initially warping space-time, while the BEBE is an example of achieving relativistic speeds that result in warped space-time. Both approaches have their problems. The main barrier to the Alcubierre drive is the enormous amounts of energy and 'exotic matter' required to warp space enough to create a 'warp bubble.' This seems to be a long way off, even with the help of agencies like NASA currently researching the theories behind it. Scientists do not even know if this so-called 'exotic matter' even exists.
The main problem for the BEBE is the ToSR itself. Einstein's equations seem to imply that any object with mass is incapable of reaching the SOL as it would require an infinite amount of energy to do so. There is no amount of efficiency an engine can have that can output infinite energy. The fuel will eventually run dry. More research needs to be done to find out if the relativistic effects from travelling at such speeds could potentially offer a loophole in Einstein's equations by warping space-time with its incredible energy, and is beyond the scope of this article. Nonetheless, due to most of claims in BEBE are unknown until published, we will wait and see to make our final conclusion if in fact the infinitive energy required in such solution is potentially available within the energy density of nuclear fuel because of anti-gravity acceleration has the leveraged effect to overcome the otherwise infinitive demand on energy supply.
There are plenty of similarities between these two approaches. Their physics are related but they employ different methods of execution. Both have their problems and their strengths and are experiencing serious scientific research for the first time. These technologies are in their early infancy, but we are learning more every day. You are encouraged to draw your own conclusions from what has been presented here. I believe that one day we will travel among the stars. I hope the day comes sooner, rather than later.