In his seminal article in 1923, Taylor demonstrated that in a viscous fluid between two coaxial rotating cylinders (Taylor--Couette flow), the curvature of the flow, or, equivalently, the centrifugal force, is a source of instability, potentially leading to vortices stacked in the annular gap \citep{Taylor}. In this work, we are rather interested in the stability of flows in rotating-disk cavities, which can be seen as flattened Taylor--Couette set-ups, of aspect ratios $\Gamma=h/\Delta R\ll1$, with $h$ the height of the cavity and $\Delta R= R_{out}- R_{in}$ the width of the annular gap. Studied for more than a century in the field of geophysics \citep{Ekman} and still present in a wide variety of industrial systems to optimize \citep{Launder}, from electronic and automotive industry to turbo-machinery in aeronautics, flows over rotating disks present a great diversity of complex instability behaviours that make them a still attractive and relevant topic of research. While the primary instabilities are now well characterised experimentally, theoretically and numerically, their role in the transition mechanisms to turbulence remains an open question that still challenges the scientific community. In this presentation, we will review the main results of the literature related to the instabilities and the main scenarios currently assumed to describe the flow breakdown to turbulence over rotating single-disks and in rotating cavities, with two generic configurations for this latter: the rotor-stator cavity and the open co-rotating cavity with radial throughflow \citep{Martinand}. Although the cavities have some specificities mainly due to the flow confinement in both radial and axial directions that may introduce some feedback mechanisms between the boundary layers, we will try to show the links that exist between the configurations, both in terms of base flows and instability mechanisms and routes to turbulence that seem to emerge in the most recent studies.