Results of a systematic examination of InAs island formation on GaAs(100) as a function of deposition conditions and thickness are presented. A non-Arrhenius dependence of the island density on substrate temperature and a decrease in the island density with increasing As4 Pressure at lower substrate temperatures is observed, indicating that currently popular frameworks of compound semiconductor molecular-beam epitaxical growth and island formation mechanism(s) need to be enlarged. Plan-view transmission electron microscopy (TEM) and use of the behavior of Moire fringes provides the island size distribution and demarcation between coherent and incoherent islands. Photoluminescence (PL) behavior is shown to vary significantly with the growth conditions and to correlate to the attendant structural nature revealed by TEM. The issue of lateral quantum confinement (i.e., three-dimensional islands as quantum boxes) is shown to be subtle and complex, calling for caution in interpreting PL behavior. The results suggest that a regular array of "quantum boxes" made of coherently strained volumes of uniform size may be achieved via growth on prepatterned mesas.