The development of turbulence is investigated in the presence of a mean plane shear flow (rate S) rotating with angular velocity vector (rate Ω) perpendicular to its plane. An important motivation was generalizing the work by Lee, Kim & Moin (1990) to rotating shear flow, in particular detailed comparisons of homogeneous rapid distortion theory (RDT) results and the databases of homogeneous and channel flow direct numerical simulations (DNS). Linear analysis and related RDT are used starting from the linearized equations governing the fluctuating velocity field. The parameterization based on the value of the Bradshaw–Richardson number B=R(1+R) (with R=−2Ω/S) is checked against complete linear solutions. Owing to the pressure fluctuation, the dynamics is not governed entirely by the parameter B, and the subsequent breaking of symmetry (between the R and −1 −R cases) is investigated. New analytical solutions for the ‘two-dimensional energy components’ [Escr ](l)ij =Eij(kl=0, t) (i.e. the limits at kl=0 of the one-dimensional energy spectra) are calculated by inviscid and viscous RDT, for various ratios Ω/S and both streamwise l=1 and spanwise l=3 directions. Structure effects (streak-like tendencies, dimensionality) in rotating shear flow are discussed through these quantities and more conventional second-order statistics. In order to compare in a quantitative way RDT solutions for single-point statistics with available large-eddy simulation (LES) data (Bardina, Ferziger & Reynolds 1983), an ‘effective viscosity’ model (following Townsend) is used, yielding an impressive agreement.