Phase vocoder
An algorithm that chops audio into overlapping windows, recomputes each window's spectrum and phase, and reassembles them at a new tempo or pitch.
James Flanagan and Roger Golden at Bell Labs described the method in 1966 as a way to compress speech. The signal is split into short overlapping windows, each run through an FFT. Moving the magnitude in each frequency bin is easy; phase is the hard part. By measuring how phase advances between windows, the algorithm works out the precise frequency in each bin and can then stitch the windows back together at a different spacing — longer sound, same pitch.
Mark Dolson's 1986 tutorial turned it into the standard tool for time-stretching. Its signature flaw is "phasiness": smeared transients and a voice that seems to be talking from inside a cardboard box. Laroche and Dolson's phase locking in 1999 helped a great deal. With the vocoder it shares little beyond the name.