Variations and extensions of the basic vertex-colouring and edge-colouring models have been developed to deal with increasingly complex scheduling problems. We present and illustrate them in specific situations where additional requirements are imposed. We include list-colouring, mixed graph colouring, co-colouring, colouring with preferences, bandwidth colouring, and present applications of edge-colourings to open shop, school timetabling and sports scheduling problems. We also discuss balancing and compactness constraints which often appear in practical situations.