Enabling "Snapping" in QGIS while drawing polygons?

In Settings / Options / Digitizing, you can define the distance radius in pixel or map units to snap to other points.

And in Settings / Snapping options you can choose which layers can be used for snapping.

In QGIS 3.12, find this under Project > Snapping options and a new (possibly docked) window "Snapping and Digitizing Options" will appear (in my case, under the Layers panel).

The only thing that does not work is snapping to the points of a line or polygon you are just creating.

Software version: QGIS 2.18.20

Note that in the latest QGIS release snapping options is no longer visible by default. To use it right-click settings to activate snapping options.