Our recent work on the electronic and optical properties of semiconductor and graphene quantum dots is reviewed. For strained self-assembled InAs quantum dots on GaAs or InP substrate atomic positions and strain distribution are described using valence-force field approach and continuous elasticity theory. The strain is coupled with the effective mass, k · p, effective bond-orbital and atomistic tight-binding models for the description of the conduction and valence band states. The single-particle states are used as input to the calculation of optical properties, with electron-electron interactions included via configuration interaction (CI) method. This methodology is used to describe multiexciton complexes in quantum dot lasers, and in particular the hidden symmetry as the underlying principle of multiexciton energy levels, manipulating emission from biexcitons for entangled photon pairs, and optical control and detection of electron spins using gates. The self-assembled quantum dots are compared with graphene quantum dots, one carbon atom-thick nanostructures. It is shown that the control of size, shape and character of the edge of graphene dots allows to manipulate simultaneously the electronic, optical, and magnetic properties in a single material system. ; peer reviewed: yes ; NRC Pub: yes