The Hofstadter Hamiltonian describes an electron moving on a two-dimensional lattice under the influence of a perpendicular magnetic field. It has been important for the theory of integer quantum Hall effect. This model, and the related almost-Mathieu maps, are a popular playground in the area of Schr?dinger operators, dynamical systems, quantum groups, etc. A famous plot, known as the Hofstadter butterfly, displays striking self-similarity properties of the spectrum. The appropriate approach to such phenomena, developed first in the theory of critical phenomena, is renormalization. In this talk, besides introducing the models, describing phenomena, and showing interesting plots, I will describe a "universality" conjecture and proofs in special cases. Some of these proofs are computer-assisted.