Paul Jewett has a helpful, short discussion of Process theology in his God, Creation, and Revelation (Eerdmans, 1991 or Wipf & Stock, 2000, pp. 281-3). For those interested in what excited the intellectual energies of 20th century theologians, here is an excerpt, with reference to Berkhof, Barth, and Brunner:
Hendrikus Berkhof, who offers no treatment as such of the doctrine of the Trinity in his Christian Faith, ends his discussion of Christology with a section entitled “The Covenant as Tri-(u)nity.” Here he observes that the three names “Father-Son-Spirit, or, with equal validity, of Father-Spirit-Son, proves to be the summarizing description of the covenantal event, both as to its historical and its existential aspect….With the term ‘Trinity’ we point to a continuing and open event, directed to man,” an event in which we participate as we are conformed to the image of the Son through the Spirit. Thus we see how God has “made himself changeable. Together with us he is involved in a process, which also does something to him because as Father it enriches him with sons and daughters” (Christian Faith, Eerdmans, 1986, pp. 335-7). Thus in Berkhof’s theology the triune God of the Creed becomes a triune event; rather than ruling over history, God is enriched by history. His name is not “I AM WHO I AM,” but “I am becoming who I hope to be.”
Barth’s thought that God’s being is “being as event” reflects, we might note, an entirely different agenda from that of Process thought. Barth is interested in the contrast between Aristotle’s Unmoved Mover and the Christian God. The latter, he argues, is a trinitarion fellowship and this fellowship is an event, internal to himself, an event that is the ontological ground of the external event of historical revelation. (See also E. Jüngel, The Doctrine of the Trinity, Grand Rapids: Eerdmans, 1976.) Along the same lines Brunner observes that while God, in contrast to the Platonic deity, hears prayer and so enters into the human event, such an accompanying (mitgehen) of our temporal order does not mean that God is subject to that order.
“His accompanying a temporal event by no means signifies that favored notion of moderns: the becoming God. The concept of a becoming God is a mythological game. Were God himself one who becomes, all would sink in the morass of relativism….A changing God is no God to whom we can pray, but a mythical being who provokes our sympathy.” (Dogmatik, I, p. 275)
I love that quote from Brunner. Jewett does a great job of succinctly culling from the broader scholarship on any given topic, which makes his systematics rather helpful as a refresher (or upper-level introduction).