Before we get too deep into a discussion on musicology we should make a note that much of our discussion will be limited to the traditions of Western Europe. There are many rich cultural traditions outside of these boundaries, however, much of our current musical traditions come from these European roots.
Eventually, musicians began to add more to these monophonic melodies. This happened in two main ways: imitative and free polyphony.
As these traditions grew, eventually the fugue, the pinnacle of polyphonic music, was developed. The fugue introduces each voice in imitative polyphony but they then diverge into free polyphony. The structure of a fugue can vary greatly from piece to piece, but the undisputed king of the fugue was J.S. Bach.
Homophony was around long before it was formalized in Rameau’s Treatise on Harmony reduced to its natural principles in the form of folk music and troubadours. After a while, the dense texture of polyphonic music began to loose its mass appeal and composers began favoring the clarity of a homophony.