  Based on the classical Pl\"ucker correspondence, we present algebraic and
geometric properties of discrete integrable line complexes in $CP^3$.
Algebraically, these are encoded in a discrete integrable system which appears
in various guises in the theory of continuous and discrete integrable systems.
Geometrically, the existence of these integrable line complexes is shown to be
guaranteed by Desargues' classical theorem of projective geometry. A remarkable
characterisation in terms of correlations of $CP^3$ is also recorded.
