In this talk we will review how cosmic strings appear as solitonic solutions in many models of high energy physics beyond the Standard Model. We will also describe the main ingredients for the cosmological formation and evolution of a network of strings. We will then discuss the latest results from large scale simulations of these networks and their implications for the expected stochastic background of gravitational waves. Finally we will comment on the current bounds on these models coming from current and future gravitational wave observatories.