Large linear systems in saddle point form arise in many applications throughout computational science and engineering. The mixed finite element methods in fluid and solid mechanics are typical examples of saddle point problems. The indefiniteness of their matrices makes it hard to solve the systems. In this talk, we will present various numerical solution techniques for this type of systems, with an emphasis on iterative methods and preconditioning techniques for large and sparse problems. This expository talk will be useful to graduate students as an introduction to this rich and important subject.