In this chapter, we study convex-concave bilinear saddle point problems. We begin by analyzing the primal-dual hybrid gradient method, providing a convergence analysis under specific conditions and carefully chosen step sizes. Next, we examine the primal-dual splitting method introduced by Chambolle and Pock, establishing its convergence under constant step sizes. Finally, we explore a primal-dual splitting method with adaptive step sizes, which eliminates the need for prior knowledge of the matrix norm involved in the problem.