  Strontium titanate is a wide-gap semiconductor avoiding a ferroelectric
instability thanks to quantum fluctuations. This proximity leads to strong
screening of static Coulomb interaction and paves the way for the emergence of
a very dilute metal with extremely mobile carriers at liquid-helium
temperature. Upon warming, mobility decreases by several orders of magnitude.
Yet, metallicity persists above room temperature even when the apparent
mean-free-path falls below the electron wavelength. The superconducting
instability survives at exceptionally low concentrations and beyond the
boundaries of Migdal-Eliashberg approximation. An intimate connection between
dilute superconductivity and aborted ferroelectricity is widely suspected. In
this review, we will give a brief account of ongoing research on bulk strontium
titanate as an insulator, a metal and a superconductor.
