Concrete quantum logics

Concrete quantum logics are quantum logics which allow for a set representa tion. They seem to be of significant conceptual value within quantum axioma tics and they play an important role in the theory of orthomodular structur es as set-representable orthomodular posets or lattices and they also somet imes constitute a "domain" for investigations in "noncommutative" measure t heory. This paper presents a survey of recent results on this class of logi cs. Stress is put on the algebraic and measure-theoretic aspects. Several o pen questions relevant to the logicoalgebraic foundation of quantum theorie s are posed.