The Mountain Pass Theorem is an important tool in the calculus of variations and in finding solutions to nonlinear PDEs in general. It is important not only for the theory but since publishing the Mountain Pass Algorithm (Choi, McKenna, 1993) also for numerical computations. I will give a review of the algorithm, present its generalization to problems with constraints and its connection to some other variational numerical methods. Examples of applications will include a model of traveling waves in a nonlinearly suspended beam and a model of cylinder buckling.