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The S-matrix Bootstrap originated on the idea that the S-matrix might befully constrained by global symmetries, crossing, unitarity, and analyticitywithout relying on an underlying dynamical theory that may or may not be aquantum field theory. Recently this approach was revived from a somewhatdifferent point of view. Using the same constraints, one numerically maps outthe (infinite-dimensional) space of allowed S-matrices that should contain allconsistent quantum field theories (and quantum theories of gravity). Moreover,in the best case scenario one finds special points in the space that can beidentified with a certain quantum field theory of interest. In that case, theapproach allows the numerical computation of the S-matrix without relying onthe particular Lagrangian of the theory.  In this white paper we summarize the state of the art and discuss the futureof the topic.

Snowmass White Paper: S-matrix Bootstrap