A comprehensive theory, herein named the Differential Interfacial Tension Hypothesis for the self-rearrangement of embryonic cells and tissues is presented. These rearrangements include sorting, mixing and formation of checkerboard patterns in heterotypic aggregates of embryonic cells, and total or partial engulfment, separation and dissociation of tissues. This broadly-based theory accounts for the action of all currently known cytoskeletal components and cell adhesion mechanisms. The theory is used to derive conditions for the cell and tissue rearrangements named above. Finite element-based computer simulations involving two or more cell types confirm these conditions.