Painting convincing shadows is the underrated half of lighting work. I want to discuss the shadow mechanics that I spent years getting wrong before I understood them.

Shadow shapes: a shadow shape is determined by the geometry of both the light source and the object casting the shadow. A hard point-source light (direct sun) creates shadows with defined edges. A large soft source (overcast sky) creates shadows with no defined edges.

Cast shadow vs form shadow: cast shadows fall on external surfaces. Form shadows are on the dark side of the casting object itself. These are different in character — cast shadows often have harder edges than form shadows on the same piece.

Shadow color: as discussed elsewhere, shadow color is the ambient light color. But here's the detail I always forget: shadows of different objects get the same ambient fill color. A red object and a blue object in the same scene cast shadows with the same ambient light fill, because the ambient is coming from the same sky.