The non-perturbative bootstrap constitutes a dramatic shift in viewpoint compared to the historical developments which cemented the physics community's acceptance of quantum field theory. First, there are many non-Lagrangian theories which cannot be reached from a free fixed point. Second, the operator algebra of a theory is agnostic to any particular microscopic description and should be analyzed with tools that are manifestly duality invariant. In the 2010s, an international community of theorists initiated a research program which fully appreciates these facts. Since then, modern mathematical and computational techniques have greatly expanded its scope. Tools which previously found critical exponents in condensed matter systems at record breaking levels of precision are now finding success in the old dream of bootstrapping the S-matrix for strongly coupled particles.I am involved in a two-pronged attack on theory space with one end occupied by conformal defects with a small number of relevant operators. As with efforts to combine the bootstrap with data from integrability or localization, this requires some flexibility on the form which crossing equations are allowed to take. At the other end are superconformal theories with many degrees of freedom whose correlators are dual to scattering processes in anti-de Sitter space. It turns out that many of these correlators, which are otherwise mysterious, can be fixed uniquely by taking the flat space limit and making comparisons to the amplitude literature. While doing this, it is tremendously helpful to realize that CFT correlators and S-matrices both give access to a regime dominated by Regge theory at large spin. This makes it tantalizing to look for connections in the opposite direction by using CFT techniques to learn about massive 2-2 scattering. Following the example set by the Froissart bound, a renewed understanding of dispersion relations is being driven by the bootstrap. Constraining the space of effective field theories, and significantly improving on past attempts to count string vaccua in the process, is the area in which I plan to become active next.
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