<p>The present survey is devoted to the 85th birthday of Volodymyr Volodymyrovych Khlobystov, prominent Ukrainian mathematician, renowned for his pioneering contributions to computational mathematics. He was a unique scholar who, despite severe visual deficiency (almost total blindness) managed to get profound results in the theory of operator polynomial interpolation. Together with his colleagues and numerous students, he laid the foundations of the contemporary theory of operator polynomial interpolation. The present survey, as compared with the most known works of the other authors, reveals the great depth and power of Khlobystov’s results. As the most important of his results, we can mention the creation of a new direction in the interpolation theory based on the use of continuous nodes. For the first time, this approach balanced the continuous amount of information about the interpolated object in the proposed interpolants with the continuous set of interpolation nodes. The Lagrange, Hermite, and Hermite– Birkhoff-type operator interpolation problems were solved, the conditions for existence and uniqueness of their solutions were established, the constructive description of the entire set of corresponding interpolants was proposed, a subset of interpolation polynomials preserving the polynomials of a given degree was selected, the accuracy of interpolation formulas was analyzed, and the problem of convergence of the interpolation processes was studied.</p>