Symplectic embedding problems are at the core of symplectic topology. Many results have been found involving balls, ellipsoids and polydisks. More recently, there has been progress on problems involving lagrangian products and related domains. In this talk, I explain what is known about symplectic embeddings of these domains. There are rigid and flexible phenomena and for some problems, the transition between the two happen at a surprising place. In order to get to the results, we will use the Arnold-Liouville theorem and billiard dynamics.