Monte Carlo has many uses, but path tracing is one of my favorites. Part four (thenumb.at/Rendering/) explores how Monte Carlo integration is used to simulate light transport.

Monte Carlo methods require randomly sampling complicated domains, which can be difficult in of itself.
Part three (thenumb.at/Sampling/) discusses how to create samplers using rejection, inversion, and changes of coordinates.

Monte Carlo integration lets us integrate high-dimensional functions exponentially faster than traditional methods!
Part two (thenumb.at/Monte-Carlo/) explores how and why it works.