Each episode of Star Trek lead in and out with Captain Kirk narrating, supposedly recording his Captain's Log, and each of those entries would begin with a star date which supposedly placed the events of the episode within a certain time span. Dates that are not based on the current Gregorian calendar that most non-hippies use. It turns out that, at least in the original series, those star dates were largely arbitrary. Seriously, go back and compare a couple, and it seems like episodes that aired within a week of each other were set decades apart. Weren't the crew of the Enterprise only meant to be on a five year mission? The star dates were mainly picked to sound futuristic, with the series set in a far-off future, but later series and movies tried to be more consistent with their dating. Before that happened, however, there was a long-running debate within Star Trek fandom as to what year the original series actually took place, with Roddenberry unhelpfully suggesting it was set in anywhere between 21st to 31st Centuries.