Consistency with quantum gravity can have significant consequences on low energy physics. Interestingly, it seems that not every effective field theory can be consistently coupled to quantum gravity unless it satisfies some additional consistency constraints dubbed Swampland constraints. In this talk, I will revisit such constraints and their emergence as a quantum gravity obstruction to restore global symmetries. I will then focus on the Swampland Distance Conjecture for which infinite distances in field space imply an infinite tower of states becoming exponentially light. We present new string theory evidence for this conjecture in Calabi-Yau manifolds, by identifying an infinite orbit within the spectrum of BPS states generated by a monodromy discrete symmetry at every infinite distance singularity in the moduli space. We apply the results to the complex structure and Kahler moduli spaces of Type II and M/F-theory compactifications.