**Anomalous diffusion**

The term anomalous diffusion is used in the physics literature to refer to Markov processes with the property that \(E|X_t-X_0|^2\) grows either faster or slower than linearly. In this talk I will give a survey of results in this area, including random walks and diffusion on the Sierpinski gasket and other exact fractals, and random examples such as critical percolation clusters and the uniform spanning tree.