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Current progress in quantum field theory is largely driven by the conformal bootstrap program, which aims to classify the space and properties of conformal field theories using symmetries and other fundamental constraints. In the context of the AdS/CFT Correspondence, this increasingly sophisticated endeavor doubles as a probe of foundations of quantum gravity. I will describe the current era in the holographic application of conformal field theory methods, with particular focus on the use of the conformal bootstrap to describe the spectrum and dynamics of quantum gravity and string theory beyond the classical regime.