Direct Multisearch (DMS) is a well-established class of Multiobjective Derivative-free Optimization methods, widely used by the optimization community in practical applications and as benchmark for new solvers. In this talk, the key features of DMS will be described, convergence results and worst-case complexity bounds will be provided, as well as recent developments covering the definition of a search step based in quadratic polynomial interpolation and strategies to address nonlinear constraints.