Quadratic and more generally finitely generated polynomial algebras appear to be naturally related with integrals of superintegrable models. Superintegrable models have many interesting properties from point of view of mathematics and physics. They have been connected with the full Askey scheme of orthogonal polynomials, exceptional orthogonal polynomials, Painlevé transcendents and equations of the Chazy class. I will review some of the recent year results on N-dimensional superintegrable systems. In particular a work on a higher rank quadratic algebra with an embedded structure.