The article analyzes and discusses the current state of the issue of abilities and giftedness in psychology. It is shown that over a long period of development of Russian psychology (1935-2018), there is a rather low interest of psychologists in it. Analysis of the content and number of publications in leading Russian and foreign journals over the past five years suggests a continuing decline in the interest of psychologists in the development of issues of abilities and giftedness. Nevertheless, the published works can be classified on a number of grounds: type of research (theoretical, empirical, complex), subject (kind and type of learned abilities), method (qualitative, quantitative, complex analysis), basis for addressing the issue (high achievements, school performance and etc.). The analysis allows us to assert that the leading reason for the unsatisfactory state of the problem is the absence in modern psychology of the theory of abilities and giftedness, which satisfactorily solves the problem of the structure of abilities, their interconnection, development not only in different age periods, but also in conditions of different kinds and types of activity, the interconnection of abilities with giftedness. Positively assessing the role of B.M. Teplov concept of abilities, we note that over the past decades, a lot of data has been accumulated that require updating both theoretical, methodological, and specifically applied foundations of the general theory of abilities. The article argues that the theory of abilities and giftedness by V.D. Shadrikov makes it possible to overcome the unsatisfactory state of this area of psychological knowledge, theoretically substantiate many applied works, not limiting itself to exceptionally high achievements in understanding the result of the functioning of the subject's abilities, etc. The results presented in the article will be useful not only in terms of theoretical and methodological study of the issue of abilities and giftedness, but also in the process of planning and organizing empirical research on abilities and giftedness.