NATO's 7.62x51mm rifle cartridge was introduced in the 1950s as its standard infantry cartridge. The "battle rifle" concept called for a weapon capable of firing a heavy medium calibre round on full automatic. The cartridge adopted was in fact identical to the .308 Winchester. However, it was found that there was no way to make a controllable 7.62x51mm assault rifle light enough to be practical. Weapons such as the FN FAL were big, clumsy, uncontrollable, and fragile. NATO then adopted the Remington .223 calibre as 5.56mm NATO, retaining the larger cartridge for certain sniper rifles and medium machine guns.
The Soviet 7.62x39mm rifle cartridge was designed during and immediately after World War II by Mikhail Kalashnikov for his famous AK-47 assault rifle. Both the bullet and the rifle were heavily influenced by the late-war German 7.62mm Kurz ("Kurz" meaning "short" in German). It remained the standard Soviet load until the 1970s, and is still by far the most common cartridge used around the world. Its replacement, the 5.45x39mm cartridge, is less powerful but longer ranged and more accurate.
Also known as a .30 calibre cartridge (pronounced "thirty").
7.62mm refers to the diameter of the lands in the barrel. The actual bullet is normally .308", although Soviet weapons commonly use a .310" bullet, as do older British and Japanese cartridges.