An introduction of the four classical models: the voter model, the contact process, stochastic Ising models, and the exclusion process, complemented by some variations on the classical models such as the two-stage contact process or biased and rebellious voter models, as well as some other models such as systems of branching, coalescing, and annihilating random walks and an example of a kinetically constrained model. Some well-known major results are mentioned together with many open problems and topics that are from the mathematical side and still poorly understood, such as the critical exponents associated with continuous phase transition and (in the final section) periodic behavior.