In this thesis, I apply numerical and analytical bootstrap techniques for a better understanding of quantum gravity. Each chapter is separated by subject. Chapter two is about a proof of the averaged null energy condition (ANEC) in flat spacetime for relativistic quantum field theories in more than two dimensions. The proof is based on microcausality and isolation of the ANEC in the OPE of primary operators in the lightcone limit. I discuss a no-go theorem for massive higher spin particles in chapter three. The no-go theorem is established on analytic properties of the S-matrix in the Eikonal limit. In chapter four, I explore connections between two-dimensional CFTs and three-dimensional pure gravity using the numerical bootstrap. My collaborators and I developed a fast algorithm for bootstrapping two dimensional CFTs using the modular bootstrap. By bootstrapping theories with large central charge, we found a new bound on the scaling dimension of the spectral gap. Chapter five is about the black hole information paradox. Using the replica trick for computing the entropy of Hawking radiation, we found a new saddle-point in the gravitational path integral. This saddle-point corresponds to a wormhole solution connecting different replica sheets. By including this saddle, we showed that the entropy computation is consistent with unitarity.