This paper appraises the current status of research devoted to the problem of modeling impact in multibody systems. The paper presents a focused, yet coherent overview of the problem of modeling impulsive motions initiated by impacts in multibody systems in light of the reported literature, while highlighting the key research accomplishments, unresolved problems, and pending challenges. The paper begins with a brief overview of the mechanics of contact in two-body collisions, and then proceeds to review different approaches for modeling the dynamics of impact in rigid multibody mechanical systems and multibody systems of interconnected rigid and flexible bodies. The review concludes by shedding light on some pertinent computational considerations.

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