  The non-perturbative implications of BRST quantization are examined for
$\theta$ vacua and related issues. Strong CP violation is shown to be absent
for QCD in the BRST formalism. Previous evidence for CP violation is
reexamined, and much of it is found to be inconclusive. It is proposed that
some lattice calculations be redone to clarify the situation. For the U(1)
problem, difficulties are encountered for a conventional solution within the
BRST framework. We also find problems with previous instanton and non-instanton
approaches.
