We investigate the electronic structure of a series of InAs-monolayer and submonolayer structures synthesized on both (100) and (311)A GaAs substrates by molecular-beam epitaxy. The chosen growth conditions ensure excellent structural and optical quality of the samples. Consequently, we have the opportunity to analyze the electronic properties of these ultrathin InAs layers which we explore by high-resolution x-ray-diffraction, photoluminescence (PL) and PL excitation (PLE) measurements. InAs submonolayer structures with an InAs coverage down to 0.78×1014 cm-2 give characteristic x-ray-interference spectra that evolve continuously with increasing In content. In contrast, the optical spectroscopies reveal a clear crossover from electronically disconnected InAs clusters to quantum-well behavior at an InAs coverage of about 3×1014 cm-2 for both orientations studied. The energies of the features observed in PL and LE spectra of these structures are modeled as a function of InAs layer thickness using an eight-band k.p-type effective-mass theory. The valence-band anisotropy of the bulk compounds is reflected in differences between both growth directions. In addition, our results indicate that the band offset ratio at the strained InAs/GaAs interface is orientation dependent.