The goal of this thesis is the optical investigation of ferroelectric domains and domain walls at the very local scale. For that, novel noninvasive approaches based on optical scanning probe microscopy are developed. The key properties investigated are the electrooptic\neffect for different domain orientations and refractive-index changes at single domain walls of barium titanate single crystals. The local probing of the electro-optic response is performed with strongly confined electric\nfields, applied via a conductive tip. With this approach we can not only probe different electro-optic coeffcients, but also identify all occurring domain orientations, even antiparallel ones. The application of additional bias fields by the same tip is used to investigate ferroelectric switching and domain growth by optical means. The experiments are supported by numerical modelling of the electric-field distribution and the resulting electro-optic response. The modelling shows excellent agreement with\nthe measurements, and allows us to separate the contributions of different electro-optic coeffcients and their associated electric-field components.\nFor the experimental observation of the theoretically predicted refractive-index profiles at single ferroelectric domain walls, polarization and position modulation of the optical probe is used to obtain high sensitivity to local modifications of the refractive index. An\nupper limit to the optical effect to the optical effect of a single domain wall is deduced from the experiment, which is compatible with the effect predicted by theory.