There are an increasing number of organizations developing and/or using music composed in part or in full by AI technologies. In the beginning, many of those efforts were academic in nature, but a growing number of groups are attempting to make a business model of composing music. And while there are more people doing it now than there were a couple decades ago, the idea of computer-composed music is reasonably old. One of the first computer compositions I’m aware of was in 1957.
The majority of these systems are structured just as you would expect: a large collection of compositions representing a genre or an artist are used as training data, which create some sort of generative/predictive model. In the very earliest approaches, simple Markov chains were derived from the compositions.