Holographic conformal field theories provide a window into quantum gravity. However, these field theories are difficult in their own right, and to make progress on them we need new non-perturbative methods. I will describe a general technique for combining the conformal bootstrap method with constraints from supersymmetric localization. This dramatically improves the ability of the bootstrap to constrain holographic theories. I will describe results for N = 4 super-Yang-Mills theory, for which this technique enables qualitatively new studies of observables as a function of the Yang-Mills coupling. I will also describe substantial improvements in the bootstrap of 3D ABJM theory, which enables a precise numerical study of higher-derivative corrections in M-theory.