  We develop the complete free boundary analysis for solutions to classical
obstacle problems related to nondegenerate nonlinear variational energies. The
key tools are optimal $C^{1,1}$ regularity, which we review more generally for
solutions to variational inequalities driven by nonlinear coercive smooth
vector fields, and the results in \cite{FocGelSp15} concerning the obstacle
problem for quadratic energies with Lipschitz coefficients.
  Furthermore, we highlight similar conclusions for locally coercive vector
fields having in mind applications to the area functional, or more generally to
area-type functionals, as well.
