This chapter presents some key aspects related to the modeling and simulation of contact problems in multibody mechanical systems. First, the fundamental aspects of the classical problem of contact mechanics are briefly visited. Next, the main methodologies commonly utilized to model and simulate contact-impact problems in multibody systems are presented, namely, those based on the penalty approach and the ones based on non-smooth formulation. In the sequel of this process, the pros and cons of each method are discussed. As application, particular emphasis is given to the description of the biomechanical contact problems for modeling and simulating human articulations such as the knee joint, and the description of foot-ground interaction during human gait. The generality of the contact force models in multibody dynamics are then summarized in terms of simplicity and efficiency of numerical computation.