While electronic and spectroscopic properties of self-assembled In1−xGaxAs/GaAs dots depend on their shape, height and alloy compositions, these characteristics are often not known accurately from experiment. This creates a difficulty in comparing measured electronic and spectroscopic properties with calculated ones. Since simplified theoretical models (effective mass, k·p, parabolic models) do not fully convey the effects of shape, size and composition on the electronic and spectroscopic properties, we offer to bridge the gap by providing accurately calculated results as a function of the dot height and composition. Prominent features of our results are the following. (i) Regardless of height and composition, the confined electron energy levels form shells of nearly degenerate states with a predominant orbital "s", "p", · · · character. In contrast, the confined hole energy levels form shells only in flat dots and near the highest hole level (HOMO). (ii) In alloy dots, the electrons' "s-p" splitting depends weakly on height, while the "p-p" splitting depends non-monotonically-due to alloy fluctuations. In pure, non-alloyed InAs/GaAs dots, both these splittings depend weakly on height. Further, the "s-p" splitting is larger while the "p-p" has nearly the same magnitude. For holes levels in alloy dots, the "s-p" splitting decreases with increasing height (the splitting in tall dots being about 4 times smaller than in flat dots), whereas the "p-p" splitting remains nearly unchaged. Shallow, pure non-alloyed dots have a "s-p" splitting of nearly the same magnitude, whereas the "p-p" splitting is about three times larger. (iii) As height increases, the "s" and "p" character of the wavefunction of the HOMO becomes mixed, and so does the heavy-and light-hole character. (iv) In alloy dots, regardless of height, the wavefunction of low-lying hole states are localized inside the dot. Remarkably, in non-alloyed InAs/GaAs dots these states become localized at the interface as height increases. The localized states are nearly degenerate and polarized along [110] and [110]. This localization is driven by the peculiarities of the biaxial strain present in the nanostructure.