This survey of interdisciplinary approaches to tonal theory and to the perception and analysis of tonal music demonstrates how different computational approaches are changing the landscape of tonal theory. Several models form the foundation of computer applications capable of broad usage. Individual contributions focus on timbral spectra in relation to modes, pitch-class sets in relation to tonality, neuroscientific aspects of tonal space, geometries of tonal theories, automatic chord identification, visualization of changing tonal content, relationships between metric and tonal structure, practical applications in the profiling of harmonic usage, and the assessment of authorship in specific repertories. Its contributors come from research in the history, theory, and psychology of music as well as computer science, mathematics, neuroscience, and operations research.