Agent-based models (ABMs) of multicellular systems are models in which each cell is represented individually. These models allow taking the variability between individual cells and the spatial heterogeneity of tissues on histological scales into account. In this chapter we present an overview and methodology of ABMs that are used to simulate mechanical and physiological phenomena in cells and tissues. ABMs are categorized as lattice based (cellular automata, lattice gas cellular automata, cellular Potts models), lattice free (center-based models, deformable cell models, vertex models), or hybrid, which are combinations of each of the latter. This model variety has been used to simulate a broad scale of phenomena, ranging from monolayer growth, tumor growth, wound healing, to organ modeling. Each approach has his strengths and weaknesses that we discuss here and in the next chapter together with the numerical solution methods and implementations. This chapter focuses on lattice and the next chapter on off lattice-free ABMs. The aim is to assist researchers in choosing the optimal model for the phenomenon they might want to model and understand.