Multibody dynamics deals with the study of mechanical systems composed of multiple bodies, whose motion interactions are governed by the presence of kinematic constraints and by the application of external forces. Frictional contact-impact events are among the most complex and important phenomena that can be modeled under the umbrella of multibody systems, since their behavior depend on critical factors, including geometry of the contacting surfaces, material properties of the colliding bodies, and constitutive laws utilized to mimic the contact response. This paper is aimed to present a comprehensive description of the most relevant aspects and the state-of-the-art techniques concerning the modeling collisions in multibody dynamics. For that purpose, the contact geometry, contact detection and contact resolution procedures are subjected to a critical analysis. Particular attention is given to the regularized or continuous models to treat frictional contacts in dynamical systems. Moreover, relevant numerical ingredients associated with contact-impact events in multibody systems are examined with the intent to discuss the computational accuracy and efficiency. Application examples are provided whose results allow to highlight the key features related to the modeling process of frictional contacts and impacts in multibody systems.