Flavoprotein monooxygenases (FPMOs) are single- or two-component enzymes that catalyze a diverse set of chemo-, regio- and enantioselective oxyfunctionalization reactions. In this review, we describe how FPMOs have evolved from model enzymes in mechanistic flavoprotein research to biotechnologically relevant catalysts that can be applied for the sustainable production of valuable chemicals. After a historical account of the development of the FPMO field, we explain the FPMO classification system, which is primarily based on protein structural properties and electron donor specificities. We then summarize the most appealing reactions catalyzed by each group with a focus on the different types of oxygenation chemistries. Wherever relevant, we report engineering strategies that have been used to improve the robustness and applicability of FPMOs.