The fugue represents one of the most important techniques Baroque composers used, and at the same time demonstrates the age's fondness for complex systems. One could almost say that the fugue is one of the most Cartesian of musical processes.

A fugue begins with an exposition in which the subject is stated by a single voice (voice in this case referring to any instrument, including a singer, that can play a musical melody). The subject is stated alone, without any other musical accompaniment. Immediately after this first statement, the subject is then stated in the second voice thus imitating the first. While the second voice is stating the subject, the first continues to play a counter melody (technically called a countersubject) against the subject. The subject then appears in a third voice and so on depending on how many voice parts the fugue has - three and four being the most common, though many more are certainly possible.

At intervals later in the fugue, the subject returns by being stated in one of the voice parts. It can be in any of the parts, and its appearance is not necessarily in the same predictable sequence as the opening exposition. Sections in the fugue in which the subject is not stated are called episodes. In summary, a fugue is a polyphonic process based on a subject alternating between subject statements and episodes.

The subject statements that occur later in the fugue may involve various permutations of the subject. Retrograde (played backwards), inversion (intervals of the melody are inverted…in other words, up becomes down and down become up), and inverted-retrograde (an obvious combination of the two) were all employed to create a miraculously complex musical experience both difficult to compose and perform. Another favorite device was augmentation where a subject was elongated by lengthening the note values. Lots of Baroque composers mastered the fugue process, but only the great composers transcended the academic fugue process into musical magic.