In this paper we describe the principles of several paradigms and methodologies for pricing transmission services. The paper outlines some of the main characteristics of these paradigms and methodologies such as where they may be used for best results. Due to their popularity, power flow based MW-mile and short run marginal cost pricing methodologies will be covered in some detail. We conclude the paper with examples of the application of these two pricing methodologies for pricing transmission services in Brazil. (author) 25 refs., 2 tabs.