I present a systematic study of self-assembled InAs/InP and InAs/GaAs quantum dots single particle and many body properties as a function of quantum dot-surrounding matrix valence band offset. I use an atomistic, empirical tight-binding approach and perform numerically demanding calculations for half-million atom nanosystems. I demonstrate that the overall confinement in quantum dots is a nontrivial interplay of two key factors: strain effects and the valence band offset. I show that strain effects determine both the peculiar structure of confined hole states of lens type InAs/GaAs quantum dots and the characteristic ,,shell-like structure of confined holes states in commonly considered low-strain lens type InAs/InP quantum dot. I also demonstrate that strain leads to single band-like behavior of hole states of disc type (,,indium flushed) InAs/GaAs and InAs/InP quantum dots. I show how strain and valence band offset affect quantum dot many-body properties: the excitonic fine structure, an important factor for efficient entangled photon pair generation, and the biexciton and charged excitons binding energies
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