In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.

Keywords:band preserving operator, universally complete vector lattice, σ-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation.