I will 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 evidence for this conjecture in Calabi-Yau manifolds, by studying the monodromy transformations associated to the infinite distance singularities in the moduli space. This monodromy generates an infinite orbit within the spectrum of BPS states and allow us to classify the different types of infinite distance loci. We apply the results to the complex structure and Kahler moduli spaces of Type II and M/F-theory Calabi-Yau compactifications. I will also discuss the implications for Inflation, including alpha-attractor models.