String theory got started in the late 1970s, when (in the context of strong force interactions) it was first proposed that particles might not be pointlike but extended objects, strings. String theory solidified into a well-defined subject in the mid-80s and there was an explosion of research when it was realized that strings might provide a way to a quantum theory of gravity. After all the initial excitement things slowed down a bit when it turned out that there were in fact several non-equivalent formulations of string theory - a bit embarrassing for a theory that is supposed to explain everything!
The real strings renaissance began in mid-90s with the discovery of so-called duality transformations that made it possible to relate the non-equivalent versions of the theory to each other - giving hints that the string theories of various types might be special cases of a more fundamental theory (usually referred to as M-theory, where the M may stand for magic, mystery or matrix - this is something that physicists are still debating about!). Since then, the number of string theory publications has grown enormously, and Edward Witten - quite possibly the leading physicist of today - has made the controversial claim that "the mathematics of 21st century will be dominated by string theory". Indeed, the only other serious contender for a quantum theory of gravityat the moment is loop quantum gravity.