Abstract: An excitonic insulator is a new quantum phase proposed by the Nobel Prize winner in physics Nevill Mott in the early 1960s. It is well known that excitons are bound pairs formed by electron-hole Coulomb interaction in insulator and semiconductor systems where, traditionally, the single-particle energy gap is much larger than the exciton binding energy. However, in some specific materials, such as narrow-gap semiconductors and two-dimensional materials, this is reversed and a large number of excitons are spontaneously formed in the system, which becomes an exciton insulator and is the ground state. At low concentrations, excitons can be regarded as composite bosons, a macroscopic quantum coherent phase, thus an exciton Bose-Einstein condensate can be observed at low temperatures. This paper briefly reviews the history of exciton insulators, as well as recent progresses on exciton insulator phases and spin superfluidity.