In recent years, coreless axial-flux permanent-magnet (AFPM) machines have been gaining attention. Being coreless, these machines do not experience eddy current (hence hysteresis losses) and has lower cogging torque leading to higher efficiency. However, limitations such as high leakage flux and weak mechanical structure impede its wide application. The results of a systematic review on coreless AFPM machine research is presented, wherein a total of 123 studies have been selected through the Preferred Reported Items for Systematic Reviews and Meta-Analysis (PRISMA) protocol. About 55% of the articles have been published between 2017 and 2021, indicating recent attention of the researchers on coreless AFPM machines. More than 70% (87 out of 123) of the records have been published by IEEE, which proves the quality and acceptance of the studies. In two-thirds (77 out of 123) of the studies, single-stator double-rotor has been adopted as the machine topology, and in 71.8% (84 out of 123) cases, trapezoidal shape magnets have been used in conventional array. The key research areas on coreless AFPM identified through this review are to produce an efficient design for multiphase and multistage topology and develop lightweight rotor and stator structures.