Simple Stochastic Games (SSGs), Mean Payoff Games (MPGs), and Parity Games (PGs) are three closely related families of infinite-duration games played on finite graphs. The best known algorithms for the solution of these games run in subexponential time and it is a major open problem whether they can be solved in polynomial time. In the talk, I plan to define these games, describe what is known about them and present many intriguing open problems.