A head-related transfer function (HRTF) is a mathematical model that describes the acoustic path between a sound source and a listener’s ear. Using binaural synthesis techniques, HRTFs play a crucial role in creating immersive audio experiences through headphones or loudspeakers, using binaural synthesis techniques. HRTF measurements can be conducted either with standardised mannequins or with in-ear microphones on real subjects. However, various challenges arise in, for example, individual differences in head shape, pinnae geometry, and torso dimensions, as well as in the extensive number of measurements required for optimal audio immersion. To address these issues, numerous methods have been developed to generate new HRTFs from existing data or through computer simulations. This review paper provides an overview of the current approaches and technologies for generating, adapting, and optimising HRTFs, with a focus on physical modelling, anthropometric techniques, machine learning methods, interpolation strategies, and their practical applications.