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I present a systematic study of self-assembled InAs/InP and InAs/GaAs quantum dot single-particle and many-body properties as a function of the 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 non-trivial 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 hole states in the 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 disk 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 exciton binding energies.

Valence band offset, strain and shape effects on confined states in self-assembled InAs/InP and InAs/GaAs quantum dots