The paper deals with the theory of qth-order fractal dimensions and its application to texture analysis. In particular, the state-of-the-art regarding the fractal dimension estimation for characterizing textures is presented. After, the insufficiency of the single fractal dimension is proven and the qth order fractal dimensions are introduced to overcome such drawback. The multifractality spectrum function D(q) is described, a novel algorithm for estimating such dimensions is then proposed, and its use in digital-image processing is addressed. Results on real SAR image textures are reported and discussed.