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The Wheeler -- DeWitt equation was proposed 50 years ago and until now it isthe cornerstone of most approaches to quantization of gravity. One can find inthe literature the opinion that the Wheeler -- DeWitt equation is even morefundamental than the basic equation of quantum theory, the Schr\"odingerequation. We still should remember that we are in the situation when noobservational data can confirm or reject the fundamental status of the Wheeler-- DeWitt equation, so we can give just indirect arguments in favor of oragainst it, grounded on mathematical consistency and physical relevance. Ishall present the analysis of the situation and comparison of the standardWheeler -- DeWitt approach with the extended phase space approach toquantization of gravity. In my analysis I suppose, firstly, that a futurequantum theory of gravity must be applicable to all phenomena from the earlyUniverse to quantum effects in strong gravitational fields, in the latter casethe state of the observer may appear to be significant. Secondly, I supposethat the equation for the wave function of the Universe must not be postulatedbut derived by means of a mathematically consistent procedure. One should takeinto account features of gravity, namely, non-trivial spacetime topology andpossible absence of asymptotic states. The Schr\"odinger equation has beenderived early for cosmological models with a finite number of degrees offreedom, and just recently it has been found for the spherically symmetricmodel 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 tobe very similar in these cases. The obtained results give grounds to say thatthe Schr\"odinger equation retains its fundamental meaning in constructingquantum theory of gravity.

Is the Wheeler -- DeWitt equation more fundamental than the Schr\"odinger equation?