The S-matrix is one of the central objects in quantum field theory and has gained renewed interest recently to better understand the possible structures of low-energy effective field theories, strongly-coupled systems, quantum gravity, etc. However, most of the particles have finite decay widths and thus do not appear in asymptotic states. Therefore, the standard S-matrix arguments may not be directly applied to scatterings of such unstable particles and we need to formulate “the S-matrix theory of unstable particles” to properly understand the availability of the S-matrix arguments in realistic systems. In this talk, I will talk about some progress towards this goal. In particular, I will discuss non-perturbative consequences of unitarity in scattering amplitudes of unstable　particles and their analytic properties.