Nanofibre-based optical cavities are particularly useful for quantum optics application, such as the development of integrated single-photon sources, and for studying fundamental light-matter interactions in cavity quantum electrodynamics (cQED). Although several techniques have been used to produce nanofibre-based optical cavities, focussed ion beam (FIB) milling is becoming popular; it can be used for the fabrication of complex structures directly in the nanofibre. This technique uses a highly accelerated ion beam to remove atoms from the target material with high resolution. However, it is challenging to mill insulating materials with highly-curved structures and large aspect ratios, such as silica nanofibres, due to charge accumulation in the material that leads to mechanical vibrations and misalignment issues. In this article, we highlight the main features of nanofibres and briefly review cQED with nanofibre-based optical cavities. An overview of the milling process is given with a summary of different FIB milled devices and their applications. Finally, we present our technique to produce nanofibre cavities by FIB milling. To overcome the aforementioned challenges, we present a specially designed base plate with an indium tin oxide (ITO)-coated Si substrate and outline our procedure, which improves stability during milling and increases repeatability., Comment: The manuscript has 16 pages, 9 figures, and 3 tables, and it will be submitted to Applied Physics B: Laser and Optics