The turbulent channel flow with streamwise rotation has been investigated by means of several different analytical, numerical, and modelling approaches. Lie group analysis of the two-point correlation equations led to linear scaling laws for the streamwise mean velocity. In addition it was found that a cross-flow in the spanwise direction is induced, which may also exhibit a linear region. By further analysis of the two-point correlation equation, it is shown that all six components of the Reynolds stress tensor are non-zero. In addition certain symmetries and skew-symmetries about the centreline have been established for all flow quantities. All these findings of the analysis have been verified very well by means of direct numerical simulations (DNS). The flow has also been calculated with large-eddy simulations (LES) and second-moment closure models. The dynamic LES captured most of the theoretical and DNS findings quantitatively. Except for one stress component the second-moment closure model was able to capture most of the basic trends, but no quantitative agreement could be achieved.