In this paper we apply techniques of spherical harmonic analysis to prove a local limit theorem, a rate of escape theorem, and a central limit theorem for isotropic random walks on arbitrary thick regular affine buildings of irreducible type. This generalises results of Cartwright and Woess where ${\tilde{A}}_n$ buildings are studied, Lindlbauer and Voit where ${\tilde{A}}_2$ buildings are studied, and Sawyer where homogeneous trees are studied (these are ${\tilde{A}}_1$ buildings).