The Ising model, one of the most studied models in mathematical physics, was introduced in 1925 to model ferromagnetism. In the classical 2D setting, the model assigns plus/minus spins to the sites of the square grid according to a given probability distribution, which is a function of the number of neighboring sites whose spins agree, as well as the temperature. The Potts model is its generalization into $q2$ possible values for each site. Over the last three decades, significant effort has been dedicated to the analysis of stochastic dynamical systems that both model the evolution of the Ising and Potts models, and provide efficient methods for sampling from it. In this talk I will survey the rich interplay between the behaviors of the static and the dynamical models, as they both undergo a phase transition at a critical temperature.