The paper presents a review of several commonly employed objective speech distortion measures and their relevance to subjective assessments of speech quality. Since many of the objective measures described in the paper have been covered previously in other reviews, we have concentrated primarily on three aspects. First, the philosophy of progressively constructing objective distortion measures in order to incrementally improve their capability to predict subjective quality (typically done at the expense of computational complexity). Secondly, we have concentrated on the use of objective measures as complementary tools to subjective evaluations, and thirdly, on the methods for evaluating the relative performance of different objective measures.