The biomechanical process of childbirth is necessary to usher in new lives—but it can also result in trauma. This physically intense process can put both the mother and the child at risk of injuries and complications that have life-long impact. Computational models, as a powerful tool to simulate and explore complex phenomena, have been used to improve our understanding of childbirth processes and related injuries since the 1990s. The goal of this paper is to review and summarize the breadth and current state of the computational models of childbirth in the literature—focusing on those that investigate the mechanical process and effects. We first summarize the state of critical characteristics that have been included in computational models of childbirth (i.e., maternal anatomy, fetal anatomy, cardinal movements, and maternal soft tissue mechanical behavior). We then delve into the findings of the past studies of birth processes and mechanical injuries in an effort to bridge the gap between the theoretical, numerical assessment and the empirical, clinical observations and practices. These findings are from applications of childbirth computational models in four areas: (1) the process of childbirth itself, (2) maternal injuries, (3) fetal injuries, and (4) protective measures employed by clinicians during delivery. Finally, we identify some of the challenges that computational models still face and suggest future directions through which more biofidelic simulations of childbirth might be achieved, with the goal that advancing models may provide more efficient and accurate, patient-specific assessment to support future clinical decision-making.