It is generally believed that strain relaxation in semiconductor heterostructures having a significant misfit (>2%) occurs by the formation of coherent three-dimensional islands, following the growth of one or two continuous two-dimensional monolayers in a manifestation of the Stranski-Krastanov (SK) growth mode. For the InAs-GaAs system, for which the misfit is approximate to 7.2%, we have shown that this is a very special case, at least during growth by molecular beam epitaxy, as it occurs on only one of the low index orientations, the (001), and then only under As-rich growth conditions. On,(110) and (111) surfaces, growth is always two-dimensional layer by layer and strain is relieved by the formation of misfit dislocations. Even when three-dimensional islands are formed on (001) substrates, the process is much more complex than the conventional SK mechanism would imply. We have used a combination of in situ reflection high-energy electron diffraction (RHEED) and scanning tunneling microscopy (STM) and ex situ transmission electron microscopy to follow the initial growth processes and strain relaxation mechanisms of InAs on GaAs (001), (110), and (111)A surfaces. RHEED enables us to establish the symmetry of the wetting layer, whether growth is two- or three-dimensional and the external crystallography of any three-dimensional islands. STM images obtained by rapid quenching from the growth temperature show how growth is initiated, provide quantitative data cin island formation (number density and volume), and indicate dislocation formation via strain field morphology effects. Detailed results for all three low index surfaces are presented, together with possible reasons for the major differences between them.