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The properties of n- and p-doped silicon nanocrystals obtained through ab initio calculations are reviewed here. The aim is the understanding of the effects induced by substitutional doping on the structural, electronic and optical properties of free-standing and matrix-embedded Si nanocrystals. The preferential positioning of the dopants and their effects on the structural properties with respect to the undoped case, as a function of the nanocrystals diameter and termination, are identified through total-energy considerations. The localization of the acceptor and donor related levels in the band gap of the Si nanocrystals, together with the impurity activation energy, are discussed as a function of the nanocrystals size. The dopant induced differences in the optical properties with respect to the undoped case are presented. Finally, the case of B and P co-doped nanocrystals is discussed showing that if carriers are perfectly compensated, the Si nanocrystals undergo a minor structural distortion around the impurities inducing a significant decrease of the impurities formation energies with respect to the single doped case. Due to co-doping, additional peaks are introduced in the absorption spectra, giving rise to a size-dependent red shift of the absorption spectra. [ABSTRACT FROM AUTHOR]