Article. Published in the journal Advances in Physical Sciences, 1971, t. 103, vol. 1, p. 87-119. Physicists and astrophysicists are currently engaged in the study of a huge number of different issues. In the vast majority of cases, we are talking about quite reasonable tasks, attempts, if not to solve the riddles of nature, then still learn something new. Of any such questions it is difficult to say that they are not interesting or important. And in general, it is not easy to determine in any consistent way what means “not important” and (or) “not interesting” in science. However, the hierarchy of problems and tasks actually exists. It operates in practice, is reflected in all scientific (and sometimes not only scientific) life and is visible even from the table of contents of journals. Often, the allocation of “especially important physical problems” occurs due to their potential technical or economic effect, sometimes it is due to a special mystery of the issue, but only another time is a tribute to fashion or is carried out under the influence of some incomprehensible or accidental factors. The compilation of lists of “important problems” and comments on them has already been undertaken more than once .. In such cases, meetings are usually convened or special commissions are created that sit (in order to “repress interference” they sometimes even go to rest homes) and generate rather voluminous documents. I do not undertake to make generalizations, but I can state that I have not seen anyone read these notes on the most important problems with great interest. Apparently, specialists in them there is no special need, and representatives of the wider "public" they do not seem attractive. Meanwhile, can novice physicists and astronomers, and not only them, not be interested in a simple question? where is now "hot" in physics and astrophysics? Or, In other words, CM. What problems of physics and astrophysics seem especially important and interesting at the moment? Based on the assumption, that such questions are really of interest to at least physics students, I tried to answer them in a lecture, The text is read by the readers. [DT Thus, this is not the result of the work of the commission and not even the result of any special research, as literary critics express it....... [