  The analytic conformal bootstrap is an array of techniques to characterize,
constrain, and solve strongly interacting quantum field theories using
symmetries, causality, unitarity, and other general principles. In the last
decade, bolstered by the development of new Lorentzian methods, it has been
used to solve conformal field theories at large spin; to place bounds on energy
distributions, event shapes, operator product coefficients, and other
observables; and to understand aspects of quantum gravity in anti-de Sitter
space. We review these advances and highlight several promising areas for
future exploration. Targets include developing new methods to close the gap
between numerical and analytic bounds, extending the bootstrap beyond conformal
fixed points, applications to quantum gravity and cosmology, and building on
ties to condensed matter theory and mathematics.
