Scattering amplitudes are heavily constrained by physical principles, such as causality, unitarity and locality. In this talk, we explore some of the imprints of such principles on the analyticity properties of Feynman integrals. In particular, we present formulas for the allowed singularity structure, sequential discontinuities and expansions around branch points. We will see how these constraints can in some cases completely fix the analytic function that the Feynman integral evaluates to.