Increasing demand for fluorine-containing compounds has led to a surge in the development of processes targeting the synthesis of alkyl fluorides. Catalytic methods of fluorination represent an efficient strategy to synthesise high value fluorinated compounds in a selective and efficient manner. Yet, catalytic methods of fluorination have received scant attention compared to those that do not utilise catalysis, despite the significant potential they offer in terms of improved process sustainability. In this review, we summarise the fluorination processes developed so far from a catalytic perspective, in order to highlight the achievements made to date, emphasise the pertaining challenges that continue to be faced, and hence aid the future development of more sustainable methods for the synthesis of C(sp³)–F bonds.