The modern incarnation of the analytic S-matrix is a non-perturbative approach that consist in exploring the space of S-matrix elements consistent with unitarity, analyticity, crossing symmetry and some extra physical assumptions about the mass spectrum of particles. In this talk I will discuss my work in progress to extend the recent ideas of the S-matrix bootstrap to include unstable resonances. This extension is crucial in order to apply such program to realistic particle physics questions involving unstable bound states. The goal of the program I will discuss is to uncover the space of consistent S-matrices for Higgs-like bosons.