The academic extrapolation of alternate outcomes of historical events: see virtual history.
A construction of past events which is refuted in verifiable or otherwise generally accepted sources: see historical revisionism. Support for the history is generally undocumented or poorly documented. Belief in such histories are often based in belief of a conspiracy theory to explain its lack of documentation.
History told from an alternative viewpoint of a minority, such as women or the indigenous people, rather than the "white male" majority. For example: "Herstory" or history from a female perspective.