A brief history of Algebraic K-Theory

The general method of K-theory is to take a complicated object and associate some simpler data to it, such that you can understand enough from the simple data alone. A straightforward idea which originated in the 1950's has since exploded into many different flavours in disparate fields of mathematics, including differential geometry, representation theory, and non-commutative algebra. I will discuss the development of (higher) algebraic K-theory with an aim at the current state of the art, hopefully culminating in current projects and challenges in the field.