  The conceptual definition and understanding of time, both quantitatively and
qualitatively is of the utmost difficulty and importance. As time is
incorporated into the proper structure of the fabric of spacetime, it is
interesting to note that General Relativity is contaminated with non-trivial
geometries which generate closed timelike curves. A closed timelike curve (CTC)
allows time travel, in the sense that an observer that travels on a trajectory
in spacetime along this curve, may return to an event before his departure.
This fact apparently violates causality, therefore time travel and it's
associated paradoxes have to be treated with great caution. The paradoxes fall
into two broad groups, namely the consistency paradoxes and the causal loops. A
great variety of solutions to the Einstein field equations containing CTCs
exist and it seems that two particularly notorious features stand out.
Solutions with a tipping over of the light cones due to a rotation about a
cylindrically symmetric axis and solutions that violate the energy conditions.
All these aspects are analyzed in this review paper.
