  The Wheeler -- DeWitt equation was proposed 50 years ago and until now it is
the cornerstone of most approaches to quantization of gravity. One can find in
the literature the opinion that the Wheeler -- DeWitt equation is even more
fundamental than the basic equation of quantum theory, the Schr\"odinger
equation. We still should remember that we are in the situation when no
observational data can confirm or reject the fundamental status of the Wheeler
-- DeWitt equation, so we can give just indirect arguments in favor of or
against it, grounded on mathematical consistency and physical relevance. I
shall present the analysis of the situation and comparison of the standard
Wheeler -- DeWitt approach with the extended phase space approach to
quantization of gravity. In my analysis I suppose, firstly, that a future
quantum theory of gravity must be applicable to all phenomena from the early
Universe to quantum effects in strong gravitational fields, in the latter case
the state of the observer may appear to be significant. Secondly, I suppose
that the equation for the wave function of the Universe must not be postulated
but derived by means of a mathematically consistent procedure. One should take
into account features of gravity, namely, non-trivial spacetime topology and
possible absence of asymptotic states. The Schr\"odinger equation has been
derived early for cosmological models with a finite number of degrees of
freedom, and just recently it has been found for the spherically symmetric
model which is a simplest model with an infinite number of degrees of freedom.
The structure of the Schr\"odinger equation and its general solution appears to
be very similar in these cases. The obtained results give grounds to say that
the Schr\"odinger equation retains its fundamental meaning in constructing
quantum theory of gravity.
