According to tradition, it was Tarquinius Priscus who had a canal constructed to drain the forum area and the valleys between the hills. The winding route along its whole course suggests that it was originally a stream flowing through a marshy valley. Walls were built to channel the flow, and it was probably not roofed until after Plautus's day since he referred to it as a canalis. (Despite what Livy says, it wasn't built underground from the very first.) Juvenal called the Suburan section of the sewer the crypta Suburae. Romans used the term crypta for any long, narrow vault, whether wholly or partially below the level of the earth..

The cloaca proper seems to have begun near the northwest corner of the Forum of Augustus in the Argiletum, the street that separated the Forum Romanum and the Subura. It entered the forum between the Curia and the Basilica Aemilia, crossed it at the east end parallel to the vicus Tuscus under the Basilica Julia, and zigzagged through the Velabrum to the Forum Boarium. The outlet of the Cloaca Maxima, or emissarium, was located between the Pons Sublicius and the Pons Aemilius. A map shows the course of the Cloaca Maxima from the Subura through the Forum of Nerva and the Forum Romanum to its effluence into the Tiber. A door leading to the Cloaca Maxima is situated in the eastern stairs of the Basilica Julia at the Roman Forum. Here, you can sometimes hear (and smell) the sewer.

The Cloaca Maxima was well maintained throughout the life of the Roman Empire. The use of different construction materials and various building styles suggests that the sewer system received regular attention. Walls and vaults of cappellaccio suggest the restorations of Sulla; those of Gabine stone, Agrippa. Sections in tufa, travertine, or concrete date from later Imperial times. Some sections had a flat roof while in others it was barrel vaulted. This public work was largely achieved through the use of Etruscan engineers and large amounts of semi-forced labor from the poorer classes of Roman citizens.

It was very expensive to clean and to repair the sewer system. The cost was defrayed partly by the treasury and partly by a tax called the cloacarium. The administration of the sewers was entrusted to the censors under the republic, but under the empire, officers called curatores cloacarum were appointed for that purpose. The emperors used condemned criminals to perform the labor.

One of the chapters in S.P.Q.R. takes place in the Cloaca Maxima, so a link to the game is a possibility.

Here are a few resources for additional information about the Cloaca Maxima.