The Terro-Human Future History is Piper's detailed account of the next 6,000 years of human history. 1942, the year the first fission reactor was constructed, is defined as the year 1 A.E. (Atomic Era). In 1973, a nuclear war devastates the planet, eventually laying the groundwork for the emergence of a Terran Federation, once humanity goes into space and develops antigravity technology.
The story "The Edge of the Knife" (collected in Empire) occurs slightly before the war, and involves a man who sees flashes of the future. It links many key elements of Piper's series.
Most of the stories take place during the next millennium, during the age of the two Federations. Most notable among these novels are the three Fuzzy novels (starting with Little Fuzzy), which concern the recognition of a peculiar alien species as sapient, and the efforts of the two species to learn to live together on the Fuzzies' home world of Zarathustra.
The Federation collapses in the System States War and following Interstellar Wars (a bit of which can be seen in The Cosmic Computer), leading to a lengthy interregnum, during which there is no central human power. Space Viking is set in this chaotic period.
The interregnum ends with the founding of the first Empire. At least five empires rule humanity during the next four thousand years, but only a handful of short stories (collected in Empire) depict this period. Piper generally portrays these empires as benign, ruled by enlightened despots.