Although it is rarely considered so in modern developmental biology, morphogenesis is fundamentally a biomechanical process, and this is especially true of one of the first major morphogenic transformations in development, gastrulation. Cells bring about changes in embryonic form by generating patterned forces and by differentiating the tissue mechanical properties that harness these forces in specific ways. Therefore, biomechanics lies at the core of connecting the genetic and molecular basis of cell activities to the macroscopic tissue deformations that shape the embryo. Here we discuss what is known of the biomechanics of gastrulation, primarily in amphibians but also comparing similar morphogenic processes in teleost fish and amniotes, and selected events in several species invertebrates. Our goal is to review what is known and identify problems for further research.