How to create an Overlay

The docs only show Modal and Tooltip Overlays (nerdlets) and I can only open them as nerdlets with openNerdlet, which replace the current one. The openOverlay does not work with a nerdlet ID, and the docs are unclear on what exactly the method opens: a nerdlet, an overlay, or some other type.

So, how can I open an overlay? That is, open content over the current nerdlet so that when I close it, the current nerdlet remains on the page?