In this study, a review is presented on previous work referring to analytical modeling of mechanical systems having components that come in contact during their motion in ways that involve impact and/or friction. The study is focused mostly on dynamical systems that can be represented by a finite number of degrees of freedom. First, models consisting of oscillators are considered and the contact action is represented by a combination of discrete spring and damper elements or rigid constraints. These models may also involve clearances and effects from friction forces. Then, systems involving rigid or discretized deformable components are examined. Depending on the approach chosen, a contact event is modeled in either an algebraic or a differential manner. In the former, the concept of a restitution coefficient plays a dominant role. In the latter, the Darboux-Keller method is applied, which also requires a restitution coefficient but considers the dynamics during the contact phase by using the normal impulse component as an independent variable, in place of time. The same category of systems is also examined next, separately, by considering techniques of Nonsmooth Mechanics, which are more convenient to apply in several cases, like in modeling multiple contact events. Finally, some special recent techniques developed for Filippov systems and for systems involving impact and friction are presented. The study concludes by identifying and suggesting possible topics for future research.