Time machines and traversable wormholes in modified theories of gravity

We review recent work on 156 wormhole geometries in the context of modified theories of gravity, in particular, in f(R) gravity and with a nonminimal curvature-matter coupling, and in the recently proposed hybrid metric-Palatini theory.In principle, the normal matter threading the throat can be shown to satisfy the energy conditions and it is the higher order curvatures terms that sustain these wormhole geometries.We also briefly review the conversion of wormholes into time-machines, explore several of the time travel paradoxes and possible remedies to these intriguing Cold/Hot Compress side-effects in wormhole physics.