Here we present some interesting aspects of interplay between quantum theory and functional analysis. We show that some of the deepest problems in both disciplines are unexpectedly equivalent. Starting from a historical point of view we comment on the following topics: connection between the structure of von Neumann algebras and the structure of quantum theories, construction of quantum integral and logic of quantum systems, Bell inequalities in light of Grothendieck inequality and operator space theory. Finally, we discuss bohrification and topos approach to quantum theory., Martin Bohata, Jan Hamhalter., and Obsahuje bibliografii