The mechanism of action of homeopathy has been the subject of basic research experiments carried out by biologists, physicists and chemists. Several groups in physics, biology and immunology have shown consistent effect of high dilutions.

Basic science research in homeopathy has been conducted in two main areas:

(1) in-vitro or in-vivo biological models of the action of ultra-molecular dilutions and their potential mechanisms of action, including the similia principle (the concept of treating like with like);

More about biological models…

(2) physical research on ultra-molecular dilutions.

More about physical models…

Although biomedical research indicates that very low concentrations, as low as 10^-22 M, can be biologically active (Eskinazi) and concentrations from 10^-6 to 10^-22 M lie in the range of homeopathic dilutions used in practice – there is overlap of active concentrations used in conventional biomedicine and homeopathy –, the main cause of scientific scepticism surrounding homeopathy is its use of very high dilutions, including ‘ultra-molecular dilutions’ that are diluted beyond the point at which theoretically any molecule of the starting substance is present (Avogadro’s number).
Eskinazi D (1999). Homeopathy re-revisited – is homeopathy compatible with biomedical observations? Archives of Internal Medicine, 159:1981–1986 [PubMed]

The Homeopathy Basic Research Experiments (‘HomBRex’) Database, a comprehensive database of basic research in homeopathy, contains information on experiments on biological systems in-vivo and in-vitro, in healthy or diseased states, ranging from the intact organism to the subcellular level, with measures of effect ranging from viability to molecular processes; and research on physico-chemical effects of serially agitated homeopathic preparations. It contains over 1,500 experiments in more than 1,000 original articles.

About 100 researchers from different universities and institutes in Europe are working in this domain and are members of the GIRI = Groupe Internationale de Recherches Infinitisimales = International group of researchers studying the effects of serially agitated high dilutions.

Some of the peer-reviewed literature in basic science research is listed here.