For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
for higher abelian targets
for symplectic Lie n-algebroid targets
This entry is to record the reference
This is the origin of the notion of Chern-Simons forms and their conception as secondary characteristic classes, which led to the refinement of the Chern-Weil homomorphism by Cheeger-Simons differential characters.
This is also where Chern-Simons theory derives its name from.