The Eumolpidae were descendants of Eumolpus, one of the first priests of Demeter at Eleusis, through his second son, Herald-Keryx. Through Eumolpus, they were related to either Poseidon or Hermes.
Starting about 300 BCE, the state took over control of the Mysteries, specifically controlled by two familes: the Eumolpidae and the Kerykes. This led to a vast increase in the number of initiates. The only requirements for membership were a lack of "blood guilt", meaning having never committed murder, and not being a barbarian (able to speak Greek). Men, women and even slaves were allowed to be initiated.