Supernova 1604 is the last Galactic supernova for which historical records exist. Johannes Kepler's name is attached to it, as he published a detailed account of the observations made by himself and European colleagues. Supernova 1604 was very likely a Type Ia supernova, which exploded 350 pc to 750 pc above the Galactic plane. Its supernova remnant, known as Kepler's supernova remnant, shows clear evidence for interaction with nitrogen-rich material in the north/northwest part of the remnant, which, given the height above the Galactic plane, must find its origin in mass loss from the supernova progenitor system. The combination of a Type Ia supernova and the presence of circumstellar material makes Kepler's supernova remnant a unique object to study the origin of Type Ia supernovae. The evidence suggests that the progenitor binary system of supernova 1604 consisted of a carbon-oxygen white dwarf and an evolved companion star, which most likely was in the (post) asymptotic giant branch of its evolution. A problem with this scenario is that the companion star must have survived the explosion, but no trace of its existence has yet been found, despite a deep search.