Shadows
Shadows were available until FlightGear 1.0. The feature became deprecated with the OSG based FlightGear 1.9.0. However, the shift to OSG opened up the possibility for re-implementing shadows and many other new graphical features in future FlightGear versions (such as happened with 3D Clouds).
At some point scenery object shadows was reintroduced, probably when scenery objects like for example vegetation and random buildings became rendered instantiated rather then as separate objects.
With FlightGear 2024.1 (link to changelog) aircraft shadows was reintroduced.
Shadow mapping
Shadow mapping is a technique that use a texture where distance of objects from the light has been recorded. During rendering, the distance to the light of the fragment rendered is compared to the shortest distance of the scene to the light, and if it is higher, the fragment is drawn using only ambient light. Otherwise, it is fully lit.
Project Rembrandt was a new project that implemented shadow mapping for FlightGear.
Another project which allowed aircraft developers to implement aircraft shadows was the Atmospheric Light Scattering (ALS) project.