Short recoil is the most common system used today in self-loading handguns, and it also used to be fairly popular in machine gun designs. The basic principle is that the bolt and barrel (in a handgun, slide and barrel) are locked together for an initial travel substantially less than the overall length of the cartridge. After typically a few millimeters of travel, the barrel stops and the bolt or slide is able to continue rearward to extract and eject the empty case. Short recoil can be paired with virtually any locking system, but today the Browning tilting barrel system is most common.
Short recoil has never been popular in shoulder rifle, as the reduction in mechanical accuracy from the moving barrel can be undesirable. In handguns and machine guns, this accuracy reduction is generally below the threshold of relevance.