Nanofibres are found in a broad variety of hierarchical biological systems as fundamental structural units, and nanofibrillar components are playing an increasing role in the development of advanced functional materials. Accurate determination of the mechanical properties of single nanofibres is thus of great interest, yet measurement of these properties is challenging due to the intricate specimen handling and the exceptional force and deformation resolution that is required. The atomic force microscope (AFM) has emerged as an effective, reliable tool in the investigation of nanofibrillar mechanics, with the three most popular approaches - AFM-based tensile testing, three-point deformation testing, and nanoindentation - proving preferable to conventional tensile testing in many (but not all) cases. Here, we review the capabilities and limitations of each of these methods and give a comprehensive overview of the recent advances in this field.