  I give a historical survey of the discussions about the existence of closed
timelike curves in general relativistic models of the universe, opening the
physical possibility of time travel in the past, as first recognized by K.
G\"odel in his rotating universe model of 1949. I emphasize that journeying
into the past is intimately linked to spacetime models devoid of timelike
singularities. Since such singularities arise as an inevitable consequence of
the equations of general relativity given physically reasonable assumptions,
time travel in the past becomes possible only when one or another of these
assumptions is violated. It is the case with wormhole-type solutions. S.
Hawking and other authors have tried to "save" the paradoxical consequences of
time travel in the past by advocating physical mechanisms of chronological
protection; however, such mechanisms remain presently unknown, even when
quantum fluctuations near horizons are taken into account. I close the survey
by a brief and pedestrian discussion of Causal Dynamical Triangulations, an
approach to quantum gravity in which causality plays a seminal role.
