Postmodern theology

Postmodern theology, also known as the continental philosophy of religion, is a philosophical and theological movement that interprets theology in light of post-Heideggerian continental philosophy, including phenomenology, post-structuralism, and deconstruction.
History.
Postmodern theology emerged in the 1980s and 1990s when a handful of philosophers who took philosopher Martin Heidegger as a common point of departure began publishing influential books on theology. Some of the more notable works of the era include Jean-Luc Marion's 1982 book "God Without Being", Mark C. Taylor's 1984 book "Erring", Charles Winquist's 1994 book "Desiring Theology", John D. Caputo's 1997 book "The Prayers and Tears of Jacques Derrida", and Carl Raschke's 2000 book "The End of Theology". 
There are at least two branches of postmodern theology, each of which has evolved around the ideas of particular post-Heideggerian continental philosophers. Those branches are radical orthodoxy and weak theology. 
Radical orthodoxy.
Radical orthodoxy is a branch of postmodern theology that has been influenced by the phenomenology of Jean-Luc Marion, Paul Ricœur, and Michel Henry, among others. 
Although radical orthodoxy is informally organized, its proponents often agree on a handful of propositions. First, there is no sharp distinction between reason on the one hand and faith or revelation on the other. In addition, the world is best understood through interactions with God, even though a full understanding of God is never possible. Those interactions include culture, language, history, technology, and theology. Further, God directs people toward truth, which is never fully available to them. In fact, a full appreciation of the physical world is only possible through a belief in transcendence. Finally, salvation is found through interactions with God and others.
Prominent advocates of radical orthodoxy include John Milbank, Catherine Pickstock, and Graham Ward.
Weak theology.
Weak theology is a branch of postmodern theology that has been influenced by the deconstructive thought of Jacques Derrida, including Derrida's description of a moral experience he calls "the weak force." Weak theology rejects the idea that God is an overwhelming physical or metaphysical force. Instead, God is an unconditional claim without any force whatsoever. As a claim without force, the God of weak theology does not intervene in nature. As a result, weak theology emphasizes the responsibility of humans to act in this world here and now. John D. Caputo is a prominent advocate of the movement.