In this review, we summarize our achievements in controlling and understanding the charging effects in single self-assembled CdTe quantum dots. We start with analysis of the single dot emission spectrum. For excitation densities small enough to ensure only s-shell recombination, we find that for all dots (also those reported by other groups) the same transition sequence is observed. Namely, the neutral exciton recombination has the highest energy while charged exciton and biexciton transitions are redshifted. This observation remains in a stark contrast to self-assembled InGaAs dots, where charged complexes may appear also on the high energy side of the neutral exciton. We explain the universality of the transition sequence assuming domination of the Coulomb correlations over direct, single particle interactions. Furthermore, through measurement of the recombination rates, we gain access to electron and hole wave functions and their redistributions upon changing the dot occupancy. We find that the electron wave function is rather stiff, while the hole wave function is rather soft owing to enhanced correlations in the valence band. We then corroborate these conclusions with the Stark spectroscopy, where we analyze energy shifts due to electric field imposed on dots embedded in a field effect or diode structure. Finally, we use these structures to obtain controllable tuning of the charge state. We discuss different approaches to this task and find the best tuning efficiency for a structure with enhanced valence band confinement.