Heinlein used his "Future History" series of stories (The Man Who Sold the Moon, Revolt in 2100, etc.) as a background for this novel about the 'Howard families'; the product of a centuries-long eugenics scheme started in the late 19th century by a millionaire who died young, that encouraged intermarriage between particularly long-lived families. Several centuries later, a stable and peaceful world discovers the Howards, and demands the secrets of their extended life spans, refusing to believe that the Howard Families simply chose their ancestors wisely.
This is the first appearance of Lazarus Long, who is so old that when he miscalculates his age he's off by a whole century! Although Lazarus is one of the Howards, his longevity appears to be from a spontaneous mutation, as he derives from only the second generation of the eugenic scheme. However, he appears to be naturally longer-lived than any of the other Howards. This book also has an appearance by the mathematical genius 'Slipstick' Libby, previously seen as a teenager in the short story 'Misfit'.
Hounded from the earth, the Howards hijack a star ship meant for colonization and try to find a better planet to live on. They even find a planet where aliens live. When Mary Sperling joins the natives, Lazurus decides it's time to go back to earth and claim their rights.
Heinlein returned to the Lazarus Long character towards the end of his career, making this the first title in a set of five inter-related novels involving time travel, parallel dimensions, free love, voluntary incest, and a concept that Heinlein called "pantheistic solipsism" or "world-as-myth" -- the theory that universes are created by the act of imagining them, so that somewhere even fictional worlds (Oz is one of the examples Heinlein uses) are real.