Apophatic theology - also known as negative theology - is a theology that attempts to describe God by negation, to speak of God only in terms of what may be said about God and to avoid what may not be said. In Orthodox Christianity, apophatic theology is based on the assumption that God's essence is unknoweable or ineffable and on the recognition of the inadequacy of human language to describe God. The apophatic tradition in Orthodoxy is often balanced with cataphatic theology - or positive theology and belief in the incarnation through which God has revealed himself in the person of Jesus Christ.
Apophatic description of God
Even though the via negativa essentially rejects theological understanding as a path to God, some have sought to make it into an intellectual exercise, by describing God only in terms of what he is not. One problem noted with this approach, is that there seems to be no fixed basis on deciding what God is not.
History in the Early Church
One of the first to articulate the theology in Christianity was the Apostle Paul whose reference to the Unknown God in the book of Acts (Acts 17:23) is the foundation of works such as that of Pseudo Dionysius. This is as Pseudo Dionysius so describes. Exemplars of the via negativa, the Cappadocian Fathers of the 4th century said that they believed in God, but they did not believe that God exists. In contrast, making positive statements about the nature of God, which occurs in most other forms of Christian theology, is sometimes called 'kataphatic theology'. Adherents of the apophatic tradition hold that God is beyond the limits of what humans can understand, and that one should not seek God by means of intellectual understanding, but through a direct experience of the love (in Western Christianity) or the Energies (in Eastern Christianity) of God. Apophatic theology can be also seen as an oral tradition. "It must also be recognized that "forgery" is a modern notion. Like Plotinus and the Cappadocians before him, Dionysius does not claim to be an innovator, but rather a communicator of a tradition." 
Negative theology played an important role early in the history of Christianity. Three theologians who emphasized the importance of negative theology to an orthodox understanding of God, were Gregory the Theologian, John Chrysostom, and Basil the Great. John of Damascus employed it when he wrote that positive statements about God reveal "not the nature, but the things around the nature." In addition, Maximus the Confessor maintained that the combination of apophatic theology and hesychasm - the practice of keeping stillness - made theosis possible.
It continues to be prominent in Eastern Christianity and is (see Gregory Palamas), and is used to balance cataphatic theology. Apophatic statements are crucial to much theology in Orthodox Christianity.
History in the Western Church
Negative theology has a place in the Western Christian tradition as well, although it is definitely much more of a counter-current to the prevailing positive or cataphatic traditions central to Western Christianity. For example, theologians like Meister Eckhart and St. John of the Cross (San Juan de la Cruz), mentioned above, exemplify some aspects of or tendencies towards the apophatic tradition in the West. The Cloud of Unknowing (author unknown) and St John's Dark Night of the Soul are particularly well-known in the West.