The present selection of refereed papers is dedicated to Moshe Livsic on the occasion of his 80th anniversary. It covers many areas of operator theory and its applications, reflecting the breadth and the profound impact of his work. In particular, some of his most recent ideas on 2D-systems are presented. Other contributions cover important avenues of modern operator theory in such fields as interpolation theory (also in the so-called nonstationary setting), direct and inverse problems for the string equation and for non-self-adjoint differential operators, operator models and function theory. The volume should appeal to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.