Rotating-disk flows were first considered by von Karman in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Karman's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.