The application of Artificial Intelligence technology to the field of music has always been fascinating, from the first attempts in automating human problem solving behavior till this day. Human activities related to music vary in their complexity and in their amenability of becoming automated, and for both musicians and AI researchers various questions arise intuitively, e. g.: What are music-related activities or tasks that can be automated? How are they related to each other? Which problem solving methods have proven well? In which places does AI technology contribute? Actually, the literature in the intersection of AI and music focuses on single problem classes and particular tasks only, and a comprehensive picture is not drawn. This paper, which outlines key ideas of our research in this field, provides a step toward closing this gap: it proposes a taxonomy of problem classes and tasks related to music, along with methods solving them. Keywords AI and creativity, music, problem cl...