We demonstrate the ability to control the eigenstates in single quantum dots by applying welldefined external fields. Electric fields oriented in-plane as well as perpendicular to the disc-shaped dots allow a modification of the spatial part of the excitonic wavefunction, giving access to the charge distribution in the dot. In contrast, magnetic fields modify the spin part of the wavefunction, resulting in a Zeeman splitting and a diamagnetic shift of the photoluminescence emission. We used the unique property of semimagnetic quantum dots to tailor the effective g-factor, i.e. the sensitivity of the eigenstates to external magnetic fields, by about two orders of magnitude simply by varying the Mn concentration in the dots.Introduction Semiconductor single quantum dots (SQDs) are often designated as 'artificial atoms', because their discrete energy level structure very much resembles that of 'real' atoms. In contrast to atoms, however, the eigenstates in SQDs can be modified by varying the extension or the composition of the quantum dots. For that reason, semiconductor SQDs represent a new class of materials with size dependent electronic, optical or even magnetic properties. This has caused a huge interest in such systems both from a basic physics point of view as well as due to fascinating device concepts like single electron devices, single photon sources or quantum computing. In this context, two topics are of strong interest: (i) the ability to control the occupation of SQDs with a discrete number of electrons and/or holes and (ii) the feasibility to manipulate the SQD eigenstates in a well-defined manner by using external electric or magnetic fields.The most convenient technique to vary the SQD occupation with electron-hole pairs is optical excitation. Simply by changing the excitation power, SQDs can be occupied by either one, two or even more electron-hole pairs and indeed, lots of recent publications have been devoted to optical studies on single excitons, biexcitons or multiexcitons in both, III-V [1-5] and II-VI [6-11] SQDs. In order to achieve a SQD occupation with an unequal number of electrons and holes, one may use above-barrier optical