The first part of the article is a lecture prepared for the 15th International Conference on Cosmic Rays (Plovdiv, Bulgaria, August 1977). In addition to historical aspects a number of questions are discussed in the lecture concerning the present state of the problem of the origin of cosmic rays. Among them are the following: proof of the existence of a cosmic ray halo and a radio halo of our Galaxy and a discussion of the relation between the homogeneous galactic model and the halo model as applied to radioactive nuclei (specifically, to $^{10}$Be nuclei). The Appendices present some information on the work of the 15th International Conference on Cosmic Rays and also a number of remarks complementing the lecture in the light of new data, etc.