We present a wavelet characterization of anisotropic Besov spaces B _p,q ^α(ℝ ⁿ), valid for the whole range 0 < p, q < ∞, and in terms of multi-resolution analyses with dilation adapted to the anisotropy of the space. Our proofs combine classical techniques based on Bernstein and Jackson-type inequalities, and nonlinear methods for the cases p < 1. Among the consequences of our results, we characterize B _p,q ^α as a linear approximation space, and derive embeddings and interpolation formulae for B _p,q ^α, which appear to be new in the literature when p < 1.