Scanning-gate imaging of semiconductor quantum dots (QDs) promises access to probability distributions of quantum states. It could therefore be a novel tool for designing and optimizing tailored quantum states in such systems. A detailed study of a lithographically defined semiconductor QD in the Coulomb-blockade regime is presented, making use of the scanning-gate technique at a base temperature of 300 mK. The method allows a one-by-one manipulation of electrons in the structure. The obtained images interpreted with a suitable QD model guide the way to a local investigation of the electronic interior of the QD. Future perspectives of scanning-gate experiments on QDs are discussed.