A central challenge in the field of developmental biology is to understand how mechanisms at one level of biological scale (i.e., cell-level) interact to produce higher-level (i.e., tissue-level) phenomena. This challenge is particularly relevant to the study of tissue morphogenesis, the process that generates newly formed, remodeled, or regenerated tissue structures. Morphogenesis arises from the spatially- and temporally-dynamic interactions of individual cells with each other and their local environment. Computational models have been combined with experimental efforts to accelerate the discovery processes. Agent-based modeling (ABM) is a computational technique that can be used to model collections of individual biological cells and compute their interactions, which generate emergent tissue-level results. Recently, ABM has been applied to the study of various developmental morphogenic processes, and the purpose of this review is to summarize these studies in order to demonstrate the types of advances that can be expected from pursuing a multicell ABM approach. We also highlight some challenges associated with ABM and suggest strategies for overcoming them. While ABM's application to the study of ecology, epidemiology, and social sciences has a much longer history, we suggest that the application of ABM to the study of morphogenesis has great utility, and when paired with benchtop experimentation, ABM can provide new insights and direct future experimentation.