Forty percent of general practitioners in the Netherlands practice homeopathy. With over 100 homeopathic medical schools, homeopathy is practiced in India along with conventional Western medicine in government clinics. In Britain, 42% of general practitioners refer patients to homeopaths. Two recent meta-analyses of homeopathy both indicate that there is enough evidence to show that homeopathy has added effects over placebo. Against this evidence is a backdrop of considerable scientific scepticism. Homeopathic remedies are diluted substances--some are so diluted that statistically there are no molecules present to explain their proposed biological effects (ultra-high dilutions or UHDs). Without knowledge of the evidence, most scientists would reject UHD effects because of their intrinsic implausibility in the light of our current scientific understanding. The objective of this article is to critically review the major pieces of evidence on UHD effects and suggest how the scientific community should respond to its challenge. Such evidence has been conducted on a diverse range of assays--immunologic, physiological, behavioral, biochemical, and clinical in the form of trials of homeopathic remedies. Evidence of UHD effects has attracted the attention of physicists who have speculated on their physical mechanisms. Included is a critique of several experiments that form the Benveniste affair which was sparked by a publication in Nature that advocated the existence of UHD effects of anti-immunoglobulin E (IgE) on human basophils, and is the paradigm example of how a controversial phenomenon can split the scientific community. It is argued that if the phenomenon was uncontroversial, the evidence suffices to show that UHD effects exist. However, given that the observations contradict well-established theory, normal science has to be abandoned and scientists need to decide for themselves what the likelihood of UHD effects are. Bayesian analysis describes how scientists ought rationally to change their prior beliefs in the light of evidence. Theories by Kuhn and Lakatos indicate that whether UHD effects are proved or not depends on the beliefs and behaviors of scientists in their communities. This article argues that there is as yet insufficient evidence to drive rational scientists to a consensus over UHD effects, even if they possessed knowledge of all the evidence. The difficulty in publishing high-quality UHD research in conventional journals prevents a fair assessment of UHD effects. Given that the existence of UHD effects would revolutionize science and medicine, and given the considerable empirical evidence of them, the philosophies of science tell us that possible UHD effects warrant serious investigation by conventional scientists and serious attention by scientific journals.