The TBP setting diverges from the Real World in the year 2001, when (in the setting) NASA sent a spacecraft named Beagle II to the planet Mars to retrieve soil samples. Beagle II carried an unsuspected Martian pathogen which became known as the Martian Flu Virus; unfortunately, the spacecraft exploded on re-entry to Earths atmosphere, releasing said virus into the biosphere. During this initial outbreak, some 15-20% of Earths population1/6 to 1/5 of all humanitydied. In addition to those who merely die, roughly 8% of Martian Flu sufferers go on to develop a complication called SCABS (short for Steins Chronic Accelerated Bio-morphic Syndrome) which can inflict radical bodily alterations on its victims. The 60-70% of Flu victims who neither die nor develop SCABS suffer nothing more than cold/flu-like symptoms.
There are a number of different flavors of SCABS, and it is possible for a victim to come down with more than one such flavor simultaneously. In order from most to least common: Animorphs, on whom SCABS has inflicted non-human physical traits ranging from a patch of fur on the elbow up to indistinguishable from a normal animal; gendermorphs, who acquire physical characteristics of the opposite sex; chronomorphs, whose biological age and/or rate of aging has been altered; polymorphs, who can assume different physical forms with an act of will; and inanimorphs, who somehow manage to retain sentience in physical bodies which do not qualify as living.
Most TBP stories are set 30 to 40 years after the Martian Flu made its unwelcome debut. A particularly unexplored part of TBP continuity is The Collapse, the name given to the period 2002-2003 or so. As one might expect, the Flus massive death toll caused severe disruptions to the social and technological infrastructure of pretty much every nation; even First World nations such as the United States were forced to declare martial law.
A likely social aftereffect of the Collapse is the curious lack of technological advancement in the TBP setting. There was far more technological change between the 1970s and the 2000s, or even between the 1940s and the 1970s, than the TBP setting has displayed between the 2000s and the 2030s.
While most TBP stories focus on the doings of the regular customers of a SCAB-friendly bar called the Blind Pig Gin Mill (hence, the name of the setting), it is certainly possible to look in on other parts of the Flu-altered world, which some writers have done to good effect.