Many of the most exciting open problems in high-energy physics are related to the behavior and ultimate nature of gravity and spacetime. In this dissertation, several categories of new results in quantum and classical gravity are presented, with applications to our understanding of both quantum field theory and cosmology.A fundamental open question in quantum field theory is related to ultraviolet completion: Which low-energy effective field theories can be consistently combined with quantum gravity? A celebrated example of the swampland program-the investigation of this question-is the weak gravity conjecture, which mandates, for a U(1) gauge field coupled consistently to gravity, the existence of a state with charge-to-mass ratio greater than unity.