At some point last year I looked into papers discussing the possibility of a warp drive, there's no indication that one could exist. Reason being that it would require exotic matter that probably doesn't exist (as it would violate energy conditions) and if it did would require astronomical amounts of energy. If you're interested
this paper outlines the energy requirements and
this paper which is further discussed in
this paper proposes possible ways of getting around this . The "trick" is to change the warp bubble so that it's exterior radius is microscopic yet the interior radius is large enough to accommodate your vehicle (essentially making a warp bubble that's bigger on the inside than on the out). Apparently this would greatly shrink the amount of energy needed to manageable levels. Bear in mind though they don't outline how exactly a shell could be build around a ship in such a fashion nor how the ship could leave.
However neither of these approaches fixes the other problems of a warp bubble such as requiring the construction of an exotic matter shell, superluminal signalling to steer/control the bubble and the huge amount of radiation a warp drive subjects you to. There are some interesting (but technical) objections in
this paper that apparently show that a warp drive would only be capable of very low velocities as well as highlighting other problems.
So without exotic matter that may
not even exist we are stuck to trying to make slower than light vehicles. To make an interstellar vehicle would be fantastically complex though requiring horrific amounts of energy (even if we used an antimatter rocket we would need potentially thousands-millions of tonnes for a high fraction of
c.) as well as a thorough understanding of ecology so as to make a stable environment in a closed system to keep the occupants alive.
