Only about 35 percent of ancient Rome is in open-air excavations; the rest of it lies hidden below street level. Exploring this subterranean world—whether it’s the catacombs or more intimate sites like the Roman houses on the Celio (www.caseromane.it)—is key to understanding the topographical evolution of Rome (not to mention a memorable adventure in archaeological spelunking). One of the most atmospheric sites for peeling back the lasagna-like layers of Rome is the 13th-century basilica of San Clemente (www.basilicasanclemente.com), where you descend through a musty maze of terrific Roman masonry to a Paleo-Christian church and a first-century Mithraeum. With advance notice, organizations like Roma Sotterranea (www.romasotterranea.it) and Context Rome can arrange private visits of super-insider sites like the Cloaca Maxima, which involves donning waders and navigating the sixth-century B.C. waterway that drained excess moisture from the Forum to the Tiber.