  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
