Mesh
Modifiers
There is an exporting option Apply Modifiers
to control whether mesh modifiers are applied to the exported mesh.
Shape Key
Exporting mesh shape key is supported, however exporting each shape key is almost like exporting the mesh again, so don't be surprised it takes a relatively long time.
WARNING
A lot of modifiers are not compatible with shape keys (e.g. subsurface modifier), so if you found you have incorrect shape keys exported, try to disable Apply Modifiers
and do the exporting again. Besides, it is worthwhile to report the incompatible modifier to the issue list, which helps to develop the exporter to have a more precise check of modifiers.