Almost 90 years ago, Mac Lane discovered the technique of "inductive valuations", which allows one to write down valuations on a rational function field over a discretely valued field in a particularly explicit way. The first talk will be a hands-on introduction to the theory, requiring no background beyond the definition of a discrete valuation (which we will recall). At the end of the talk, we will fast forward 80 years or so and discuss the relationship between Mac Lane valuations and models of the projective line.