Warning: Wikipedia contains spoilers
Events in Eon take place around the year 2000, when USA and USSR are on the verge of a nuclear war (the book was written prior of the fall of USSR). In the middle of the hot political climate, an asteroid appears from nowhere near Earth orbit, and the two nations fight to claim it.
The asteroid is hollow and filled with empty cities, but seems to come from Earth's future, and was terraformed by human beings. A team of scientists discovers that the asteroid is bigger inside than outside, and in particular that the last internal chamber seems to stretch into infinitum. An expedition is sent down the "tube", as it's called, where it will meet humanity descendants. The high technology of this civilization, including total control over genetic engineering, virtual worlds, human augmentation and magic-like control over matter is one of the main points of interest of this book. Several aliens species live with human beings. The human descendants are also at war with an alien race, the Jarts, a topic that will be further expanded in the second book of the series.