The Lorentz gas can be considered as a toy model for the classical dynamics of an electron in a crystal. Its fundamental dynamical properties and its relation to multibaker maps as well as to hard disk gases will be briefly discussed. In particular, we will focus on deterministic diffusion in the periodic Lorentz gas with respect to varying the density of scatterers. Computer simulation results for the diffusion coefficient will be compared to the simple random walk approximation of Machta and Zwanzig and to straightforward improvements of it. Characteristics of microscopic chaos in the diffusion coefficient will be analyzed.