Perhaps the first detailed future history was that of Robert Heinlein, who originated the term in the sense described here. His collection The Man who Sold the Moon offers a vertical timeline labeled "FUTURE HISTORY 1951-2600 A.D." with stories and novels located appropriately, lives of significant characters marked with vertical bars, and commentary. His full future history is compiled in two volumes: The Past Through Tomorrow and Orphans of the Sky.
Other notable future histories:
Also, standalone stories which trace an arc of history are rarely considered future histories. For example, neither Walter M. Miller Jr's A Canticle for Leibowitz nor Olaf Stapledon's Last and First Men are generally considered future histories.
Unlike alternate history, where alternative outcomes are ascribed to past events; future history postulates certain outcomes to future events. One problem with future history science fiction is that it will date and be overtaken by real historical events (for instance, H. Beam Piper's future history included a nuclear war in 1973). For this reason, many authors set their stories in an indefinite future, often in a society where the current calendar has been disrupted due to a societal collapse or undergone some form of distortion due to the impact of technology.
However, a number of hard science fiction writers extrapolate today's technology and events into the near future. Their stories need no fantastic technologies that have not yet been discovered but merely take the next step or two in forseeable technological advancement and ask "What If"?