Please look at some of the religious values articulated by both St. Augustine and St. Thomas Aquinas. I would appreciate your thoughts on the relevance of religious authority. How do you understand this in the modern world?

For both of these Church Fathers, the ultimate authority was God, as manifested in all three persons of the Trinity. On religious questions, God is the only and ultimate authority. For both thinkers, God revealed himself in the Bible (in Latin, Liber) and Creation, which these thinkers refer to at points as the Liber Mundi (the book of the world); Creation can be "read" or interpreted as a manifestation of God's will.
The difficult issue with authority is interpretation. In other words, it was apparent from the earliest days of Christianity that different Christians interpreted the Bible and the evidence of Creation differently. Thus, the crucial question became the locus of interpretive authority. Although Augustine advocates a complex and subtle form of hermeneutics, he also ultimately accepts that the Church is the final arbiter of interpretation. Aquinas fundamentally agrees with this position.
Augustine, in locating the locus of authority in the Roman Catholic Church, was in part attempting to heal the fractures that were splitting the Church into opposing groups. Aquinas was attempting a grand synthesis of Aristotelian science with Christianity.
Protestants argued that this notion of the Church as interpreter of the Bible led to an ossified church hierarchy that stood between believers and the source of their religion, and thus advocated a sola scriptura doctrine in which individuals read the Bible for themselves (rather than simply listening to sermons expressing the Church's beliefs about the Bible).
In the modern world, different denominations take different approaches to authority, with Roman Catholics and Orthodox Christians emphasizing the traditions of the Church (though disagreeing with one another) and many Protestant groups emphasizing the importance of individual reading and study of the Bible as a source of interpretive authority.