The Institute is run by the Royal Swedish Academy of Sciences on behalf of research societies representing all the Scandinavian countries.
At his death in 1927, however, Mittag-Leffler's fortune was insufficient to set up an active research institute, which began operation only in 1969 under the leadership of Lennart Carleson.
For a number of years at the beginning of the 20th century, Mittag-Leffler's villa hosted a celebratory dinner for Nobel Prize laureates.
Some notable past visitors include: Louis Billera, Sy Friedman, John B. Garnett, Roger Heath-Brown, Sigurður Helgason, Helge Holden, Harry Kesten, Donald Knuth, George Lusztig, Paul Malliavin, Benoit Mandelbrot, Lynn Steen, André Weil, Srinivasa S.R.
A first-edition copy of Copernicus's "De revolutionibus orbium coelestium" (On the Revolutions of Heavenly Spheres) was stolen from the Mittag-Leffler Institute.