The novel's plot is largely concerned with the so-called Fringe War. All the intelligent species of Known Space are interested in the Ringworld. In the novel (actually begun in the previous novel, The Ringworld Throne), they engage in a Cold War of sorts on the fringe of the Ringworld star system.
The novel also explores the interactions of multiple elements invented or described in previous Niven short stories or novels. For instance, two stories in the Crashlander short-story anthology consider separately the implications of a super-fast hyperdrive ("At the Core") and medical nanotechnology ("Procrustes"). Although these super-technologies are seemingly unrelated, their combination is a key element of the plotline of Ringworld's Children.
In another example, the ARM ships of the Fringe War are powered by antimatter and have antimatter weapons. When asked where they most likely got it from, the Hindmost remarks that it is probably from an antimatter solar system. This is a reference to a third short story ("Flatlander") in the Crashlander anthology that describes the discovery of the antimatter planet Cannonball Express.
Another, more obscure reference to a Beowulf Shaeffer story, "The Borderland of Sol", concerns creatures that live in hyperspace and eat spaceships in hyperspace around gravity wells, thus explaining why ships cannot safely engage their hyperdrive close to a large mass (which was previously described as a singularity before this revelation). This reference, dismissed as a myth in the earlier story, is casually confirmed as fact in this installment and is surpassed by the creation of a hyperdrive that moves the entire Ringworld to destination unknown.
As in the previous two novels, the interactions of various hominid Pak protectors play an important role, including one who claims to be one of the original builders of the ring. A number of previously revealed "facts" turn out to have been lies told by characters in the books, which is another common feature of Niven's Ringworld and other Known Space stories, especially those involving Protectors and Puppeteers.
Ringworld Prequel series (Larry Niven and Edward M. Lerner?)
Ringworld (Larry Niven)
More: The Ringworld