Aspects of Calabi-Yau integrable and Hitchin systems

In the present notes, prepared for lectures at the `Workshop on the Geometry and Physics of Higgs bundles IV' in March 2019, we explain the relation between Calabi-Yau integrable systems and Hitchin systems based on work by Diaconescu-Donagi-Pantev and the author. Besides an introduction to these integrable systems, we highlight related topics, for example variations of Hodge structures, cameral curves and Slodowy slices, along the way.