Wikipedia
Process theology is a type of theology developed from Alfred North Whitehead's (1861–1947) process philosophy, most notably by Charles Hartshorne (1897–2000) and John B. Cobb (b. 1925). Process theology and process philosophy are collectively referred to as "process thought." (Process theology is unrelated to the Process Church.)
For both Whitehead and Hartshorne, it is an essential attribute of God to affect and be affected by temporal processes, contrary to the forms of theism that hold God to be in all respects non-temporal (eternal), unchanging ( immutable), and unaffected by the world ( impassible). Process theology does not deny that God is in some respects eternal (will never die), immutable (in the sense that God is unchangingly good), and impassible (in the sense that God's eternal aspect is unaffected by actuality), but it contradicts the classical view by insisting that God is in some respects temporal, mutable, and passible.
According to Cobb, "process theology may refer to all forms of theology that emphasize event, occurrence, or becoming over against substance. In this sense theology influenced by Hegel is process theology just as much as that influenced by Whitehead. This use of the term calls attention to affinities between these otherwise quite different traditions" Also Pierre Teilhard de Chardin can be included among process theologians, even if they are generally understood as referring to the Whiteheadian/Hartshornean school, where there continue to be ongoing debates within the field on the nature of God, the relationship of God and the world, and immortality.