Epiclesis

Deriving from the Greek verb epikalein, "to summon," the Epiclesis is the name given to the prayer used especially in Eastern rites to invoke the presence of the Holy Spirit when the bread and wine are consecrated in the Eucharist. This, e.g., is the form it took in the Liturgy of Theodore of Mopsuestia:

May there come upon us and upon this oblation the grace of the Holy Spirit. May He dwell and rest upon this Bread and upon this Cup, and may He bless, consecrate, and seal them in the name of the Father and of the Son and of the Holy Spirit. By the power of Thy Name, may this Bread become the Holy Body of our Lord Jesus Christ, and this Cup the Precious Blood of our Lord Jesus Christ.

While a prayer along similar lines may be found in many Western rites, it never attained the spiritual and liturgical significance as it did in Eastern churches.