The papaer presents a review of some publications on the history of the development, formation, functions and capabilities of scientometrics, as well as the state of Russian science and its role on the international arena. The thoughts regarding the role of scientometrics in modern scientific research are stated. To date, scientometrics provides a number of possibilities. First of all, it is a system for monitoring publication activity of scientists around the world. Obviously, the main goal is structuring scientific publications with the following improvement of scientific activity. Howewer, are modern scientometric indicators objective in relation not only to the number, but also to the quality of scientific publications? Is the notorious Hirsch index an ideal parameter for evaluating the performance of researchers? Are there any prospects for scientometrics in the modern scientific world, or is a worthy alternative to currently used methods for assessing scientific activity required? These and many other questions are raised by the authors in this article.