Field theoretic models on covariant quantum spaces

This thesis is based on hep-th/0203110, hep-th/0005273, hep-th/0107068, hep-th/0106205, and hep-th/0103164, but includes additional results, details, and background material. It covers the description of D-branes on group manifolds based on quantum groups including the required mathematical background, field theory on the q-deformed fuzzy sphere (both first- and second-quantized), fuzzy instantons, and one-loop results on the fuzzy sphere.