Phagocytosis is the fundamental cellular process by which eukaryotic cells bind and engulf particles by deforming their plasma membrane. Particle engulfment involves particle recognition by cell-surface receptors, signalling, and remodelling of the actin cytoskeleton to guide the membrane around the particle in a zipper-like fashion. The signalling complexity is daunting, involving hundreds of different molecular species during the initial stages of engulfment. For instance, the well-characterized immune Fcγ and the integrin CR3 receptors signal to tyrosine kinases and Rho GTPases, ultimately regulating a wide variety of proteins, which direct actin polymerization and myosin-motor proteins for force generation and contraction. Despite the signalling complexity, phagocytosis also depends strongly on simple biophysical parameters, such as shape and cell stiffness, or membrane biophysical properties that are independent of the type of cell or particle. We argue that these emergent, universal features are particularly important to address in order to explain this evolutionary well-conserved and robust mechanism. In this chapter we review these universal features to describe the principles of phagocytosis. Specifically, we use a recently published model of phagocytic engulfment as a guide. Finally, we discuss state-of-the-art live-cell fluorescence microscopy, recently used to elucidate the dynamics of phospholipids, actin polymerization and myosins in the particle shape recognition by the amoeba Dictyostelium.