Happen, take place, as in What's going on here? [Early 1700s]
Continue, as in The show must go on. [Late 1500s]
Keep on doing; also, proceed, as in He went on talking, or She may go on to become a partner. [Second half of 1600s]
Act, behave, especially badly. For example, Don't go on like that; stop kicking the dog. [Second half of 1700s]
Also, go on and on; run on. Talk volubly, chatter, especially tiresomely. For example, How she does go on! The first usage dates from the mid-1800s; run on appeared in Nicholas Udall's Ralph Roister Doister (c. 1553): "Yet your tongue can run on."
An interjection expressing disbelief, surprise, or the like, as in Go on, you must be joking! [Late 1800s]
Approach; see going on.
Use as a starting point or as evidence, as in The investigator doesn't have much to go on in this case. [Mid-1900s]
go on something. Begin something, as in go on line, meaning "start to use a computer," or go on a binge, meaning "begin to overdo, especially drink or eat too much."