Homeopathy is based on the idea of ‘let like be cured by like’. It was founded by Samuel Hahnemann in the late 18th century, although similar concepts existed earlier. Homeopathy became popular in the 19th century in part because of its success in epidemics but declined during most of the 20th century. Its popularity increased in the late 20th and early 21st centuries in many parts of the world. Homeopathy is controversial because of its use of highly dilute medicines. There is a significant body of clinical research including randomised clinical trials and meta-analyses of such trials which suggest that homeopathy has actions which are not placebo effects. Cohort, observational and economic studies have yielded favourable results. There are several schools of homeopathy. Systems which use homeopathic medicines based on symbolism and metaphor are not homeopathy. Despite the long history of scientific controversy, homeopathy has proved resilient and is now geographically widespread. There is a significant body of scientific evidence with positive results. Homeopathy is an anomaly around which deserves further investigation.