Classical diffusion of single particles on lattices with frozen-in disorder is surveyed. The methods of continuous-time random walk theory are pedagogically developed and applications to solid-state physics are discussed. The first part of the review treats models with regular transition rates; these models possess internal structure or correlations over two jumps and complete solutions are given for each case. The second part of the review covers models with disorder in the transition rates and irregular lattices. For these problems too, explicit calculations and methods are explained and discussed.