Gregory of Nanzianzus (ca. 330-389), lived during a period in which there were intense controversies about the nature of Christ and of the Trinity. He was born shortly after the Council of Nicaea, also known as the first ecumenical council, and was a participant in the second ecumenical council, the Council of Constantinople, in 381. The major theological debates addressed in these controversies had to do with Christ and his role in the Trinity.
The first debate was over whether all members of the Trinity were in fact equal or whether the Son, being begotten and not eternal, was in some way lesser than the Father, and of a similar substance (homoiousia) to the Father but not the same substance (homoousia). The Council of Nicaea represented a victory for the homoousian (same substance) party, and Arianism was condemned as a heresy. Gregory was of the homoousian or Nicaean party in the ongoing debate.
Another issue raised in this period was whether, given that Christ had a divine and human nature, that meant that the father suffered on the cross (the Patripassian heresy) as the Son suffered due to their shared divine nature (something Gregory did not believe). Gregory, as an orthodox Nicaean would also have disbelieved the Docetist position that the human form of Christ was merely an illusion and the Christ was purely divine in nature.