In this paper we present an overview of agent based models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings and capabilities of the major agent based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.