The Society's headquarters are in Marloes Road, London.
It publishes the quarterly Journal of the Society for Psychical Research (JSPR), the irregular Proceedings and the magazine Paranormal Review. It holds an annual conference, regular lectures and two study days per year. Its French equivalent, the French Society for Psychical Research, publishes the Journale de la Société Française pour Recherche Psychique (JSFRP), which means "Journal of the French Society for Psychical Research" in English. Its American counterpart, the American Society for Psychical Research, publishes the Journal of the American Society for Psychical Research (JASPR).
| The presidents of the Society for Psychical Research | |
| 1882-1884 | Henry Sidgwick (1838-1900), philosopher |
| 1885-1887 | Balfour Stewart (1827-1887), physicist |
| 1888-1892 | Henry Sidgwick (→ 1882) |
| 1893 | Arthur Balfour (1848-1930), later Prime Minister of the United Kingdom, originator of the well known Balfour Declaration |
| 1894-1895 | William James (1842-1910) psychologist, philosopher |
| 1896-1899 | Sir William Crookes (1832-1919), physicist, chemist |
| 1900 | Frederick William Henry Myers (1843-1901), philologist and philosopher |
| 1901-1903 | Sir Oliver Lodge (1851-1940), physicist |
| 1904 | Sir William Fletcher Barrett (1845-1926), physicist |
| 1905 | Charles Robert Richet (1850-1935), physiologist, Nobel Prize winner |
| 1906-1907 | Gerald Balfour (1853-1945), politician, brother of Arthur Balfour |
| 1908-1909 | Eleanor Sidgwick (1845-1936), mathematician, wife of Henry Sidgwick, sister of Arthur Balfour |
| 1910 | Henry Arthur Smith (1848-1922), lawyer |
| 1911 | Andrew Lang (1844-1912), anthropologist and writer |
| 1912 | William Boyd Carpenter (1841-1918), Bishop |
| 1913 | Henri Bergson (1859-1941) philosopher; Nobel Prize winner for literature 1927. |
| 1914 | Ferdinand Canning Scott Schiller (1864-1937), philosopher |
| 1915-1916 | George Gilbert Aime Murray (1866-1957), philologist |
| 1917-1918 | Lawrence Pearsall Jacks (1860-1955), professor of philosophy in Oxford |
| 1919 | John Strutt, 3rd Baron Rayleigh (1842-1919), physicist, Nobel Prize 1904 |
| 1920-1921 | William McDougall (1871-1938), psychologist |
| 1922 | Thomas Walter Mitchell (1869-1944), editor of the British journal of medical psychology |
| 1923 | Camille Flammarion (1842-1925), astronomer |
| 1924-1925 | John George Piddington (1869-1952), businessman |
| 1926-1927 | Hans Driesch (1867-1941), German biologist and natural philosopher |
| 1928-1929 | Sir Lawrence Jones (1885-1955) |
| 1930-1931 | Walter Franklin Prince (1863-1934), clergyman |
| 1932 | Eleanor Sidgwick (→ 1908) and Oliver Joseph Lodge (→ 1901) |
| 1933-1934 | Edith Lyttelton (born Balfour; 1865-1948), playwright |
| 1935-1936 | C. D. Broad (1887-1971), philosopher |
| 1937-1938 | Robert Strutt, 4th Baron Rayleigh (1875-1947), physicist |
| 1939-1941 | Henri Haberley Price (1899-1984), philosopher |
| 1942-1944 | Robert Henry Thouless (1894-1984), psychologist |
| 1945-1946 | George N. M. Tyrrell (1879-1952), mathematician |
| 1947-1948 | William Henry Salter (1880-1969), lawyer |
| 1949 | Gardner Murphy (1895-1979), psychologist |
| 1950-1951 | Samuel George Soal (1889-1975), mathematician |
| 1952 | Gilbert Murray (→ 1915) |
| 1953-1955 | Frederick Stratton (1881-1960), astrophysicist, professor in Cambridge |
| 1956-1958 | Guy William Lambert (1889-1984), diplomat |
| 1958-1960 | C. D. Broad (→ 1935) |
| 1960-1961 | Henri Habberley Price (→ 1939) |
| 1960-1963 | Eric Robertson Dodds (1893-1979), professor of Greek studies in Birmingham and Oxford |
| 1963-1965 | Donald James West (* 1924), psychiatrist and criminologist |
| 1965-1969 | Sir Alister Hardy (1896-1985), zoologist |
| 1969-1971 | W. A. H. Rushton (1901-1980), physiologist, professor in Cambridge |
| 1971-1974 | Clement William Kennedy Mundle (* 1920), philosopher |
| 1974-1976 | John Beloff (1920-2006), psychologist at the University of Edinburgh |
| 1976-1979 | Arthur J. Ellison (1920-2000), technologist |
| 1980 | Joseph Banks Rhine (1895-1980), biologist and parapsychologist |
| 1980 | Louisa Ella Rhine (1891-1983), parapsychologist, wife of Joseph Rhine |
| 1981-1983 | Arthur J. Ellison (→ 1976) |
| 1984-1988 | Donald James West (→ 1963) |
| 1988-1989 | Ian Stevenson (1918-2007), psychiatrist |
| 1989-1992 | Alan Gauld, psychologist |
| 1993-1995 | Archie Roy, professor of astronomy in Glasgow, founded the Scottish SPR in 1987 |
| 1995-1998 | David Fontana, professor of psychology at Cardiff University |
| 1998-1999 | Donald James West (→ 1963, → 1984) |
| 2000-2004 | Bernard Carr, professor of mathematics and astronomy at Queen Mary, University of London |
| 2005-2007 | John Poynton, Biologist |
| 2007- | Deborah Delanoy, parapsychologist |
The Society has many well known figures among its members, including Dean Radin, Peter Underwood, Charles Tart, Tom Ruffles, Ciarán O'Keeffe, and Louie Savva. Investigators of spontaneous phenomena (hauntings, etc.) include the late Maurice Grosse and Guy Lyon Playfair who investigated reports of the Enfield Poltergeist.