Permanent magnet (PM) machines have been extensively used for various applications. Nevertheless, thermal effect, particularly hotspot temperature, not only severely restricts power/torque density but also leads to deteriorations in electromagnetic performance, service life, and reliability. Starting with foundations of PM machines and heat transfer mechanisms, this paper reviews the development of thermal analysis methods over the last thirty years and the state-of-the-art research achievements, and the hotspot temperatures of winding and PM are particularly evaluated. In the overview, various machine losses and cooling techniques are first introduced, which are the essential reasons for temperature rise and the most straightforward way to remove the generated heat. Afterwards, the mainstream thermal analysis techniques, i.e., numerical techniques, lumped-parameter thermal model, and hybrid thermal models, as well as the online electrical parameter-based and thermal model-based temperature monitoring techniques, are reviewed and assessed in depth. In addition, this paper also reviews the analytical thermal modelling methods for winding and PM. Finally, future research trends are highlighted.