A fully quantized model of atom--field interactions requires both the atom and field to be quantized. The impetus for developing this theory is to examine an atom interacting with a weak electromagnetic field in a cavity because the semiclassical theory requires that the field be strong. The situation of an atom interacting with a weak cavity field is becoming very important in atomic physics because it is being used to test fundamental assumptions about complementarity, uncertainty, and other concepts which lie at the heart of the quantum mystery. A fully quantized atom--field model can be constructed once we have developed an understanding of the quantum field in a cavity. In this chapter, we are concerned with cavity fields, and this theory, not a general theory, will be discussed.