  "Warp drive" spacetimes and wormhole geometries are useful as
"gedanken-experiments" that force us to confront the foundations of general
relativity, and among other issues, to precisely formulate the notion of
"superluminal" travel and communication. Here we will consider the basic
definition and properties of warp drive spacetimes. In particular, we will
discuss the violation of the energy conditions associated with these
spacetimes, as well as some other interesting properties such as the appearance
of horizons for the superluminal case, and the possibility of using a warp
drive to create closed timelike curves. Furthermore, due to the horizon
problem, an observer in a spaceship cannot create nor control on demand a warp
bubble. To contour this difficulty, we discuss a metric introduced by
Krasnikov, which also possesses the interesting property in that the time for a
round trip, as measured by clocks at the starting point, can be made
arbitrarily short.
