Harmonic tori and their spectral data

This is an expository article which describes one approach to the construction and classification of harmonic tori “of finite type”, namely, via their ring of polynomial Killing fields. To keep the discussion focussed, the first section is devoted entirely to non-conformal harmonic tori in the 2-sphere. The second section summarizes the authors more recent work on pluri-harmonic maps into complex Grassmannians.