Disordered systems are mathematical models (typically of the physical world) that are governed by random variables.  These models have offered insights into a diverse array of research problems, and have also brought about a great number of powerful mathematical tools.  The through line to the subject is the essential role played by probability theory, a relatively modern invention.  By inserting random variables into classical models of physics, one finds new capacities for understanding the natural world.  This talk will provide vignettes of three such models: disordered geometry, disordered motion, and disordered magnetism. This tour of disordered systems will introduce some recurring technical themes such as Gibbs measures and variational formulas, which animate (for us mathematicians) this immensely rich subject.