In the paper we present a selected variety of problems studied by Professor Jerzy Zabczyk. Important part of Prof. Zabczyk's scientific activity was devoted to his PhD students. He has promoted 9 PhD students: Tomasz Bielecki, Jarosław Sobczyk, Łukasz Stettner and Gianmario Tessitore work mostly in control and its applications to mathematical finance, whereas the research of Anna Chojnowska-Michalik, Wojciech Jachimiak, Anna Milian, Szymon Peszat and Anna Rusinek is concentrated mostly on stochastic evolution equations. Description of research problems of Prof. Jerzy Zabczyk starts from infinite-dimensional (deterministic) control problems, stochastic control problems: optimal choice problems, stopping time problems, to come first to mathematics of finance and then to stochastic analysis: stochastic evolution and partial differential equations. We show main results and point out their importance. The paper is based on the presentation of the authors during a special session at the conference.