The paper provides an overview of the main research works of Professor V. L. Kharitonov. Seven topics have been distinguished: stability analysis of families of polynomials, stability analysis of families of quasipolynomials, the problem of the critical delay, a generalization of the Lyapunov matrix equation, analysis of multivariate polynomials, the theory of complete type functionals for time-delay systems, and prediction-based control. Basic concepts and theorems are given for each topic, the main ideas and results obtained by V. L. Kharitonov are described, corresponding references are given. We tried to make the text understandable not only for specialists in control theory but also for students who have basic knowledge in the theory of differential equations and in the stability theory.