Sum of squares (SOS) programs are a particular class of convex optimization problems, that combine in a very appealing way notions from algebraic and numeric computation (in particular, semidefinite programming). They are based on the sum of squares decomposition for multivariate polynomials, and have found many interesting applications, mainly through semidefinite relaxations of polynomial optimization problems. In this talk we will quickly review the basic SOS framework, focusing on the SOSTOOLS toolbox (developed in collaboration with Stephen Prajna, Antonis Papachristodoulou, and Pete Seiler). The ideas and algorithms will be motivated and illustrated via interesting new applications, including Systems and Control, quantum information, and game theory.