Abstract: Lattice-free agent-based models (ABMs) of multicellular systems are mathematical models in which each cell is represented individually and can move continuously in space. In this chapter we present an overview of the methodology of ABMs that are used to simulate mechanical and physiological phenomena in cells and tissues. Lattice-free models are roughly categorized as center-based models, deformable models, or hybrid approaches. This model variety allows to simulate a broad scale of phenomena, ranging from monolayer growth, tumor growth, wound healing, to organ modeling. However, every approach brings its own difficulty and demands a particular care and expertise. We discuss here numerical solution methods and implementations to describe the dynamics in the different models.