Complex cobordism and its relatives, the Johnson-Wilson theories, E(n), carry an action of C_2 by complex conjugation. Taking homotopy fixed points of the latter yields Real Johnson-Wilson theories, ER(n). These are generalizations of real K-theory and are similarly amenable to computations. We will outline their properties, describe a generalization of the \eta-fibration, and survey some recent computations of the ER(n)-cohomology of well-known spaces, including complex projective spaces, classifying spaces of certain compact Lie groups, and Eilenberg-MacLane spaces.