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

Closed Timelike Curves, Singularities and Causality: A Survey from G\"odel to Chronological Protection