Abstract: While object deformation has received a lot of attention in Computer Graphics in recent years, with several good surveys that summarize the state-of-the-art in the field, a comparable comprehensive literature review is still needed for the related problem of crack and fracture modeling. In this paper we present such a review, with a special focus on the latest advances in this area, and a careful analysis of the open issues along with the avenues for further research. With this survey, we hope to provide the community not only a fresh view of the topic, but also an incentive to delve into and explore these unsolved problems further.