Applications of the Savonius rotor have been extended in recent years, necessitating an in-depth investigation on flow characteristics of such a fluid energy converting device. For the wake flow downstream of the Savonius rotor, studies have been reported extensively. Nevertheless, literature specifically devoted to the upstream flow of the Savonius rotor can rarely be found. This review collects and compiles findings from relevant studies to prove the significance of upstream flow patterns to the operation of the Savonius rotor. Then attempts from experimental and numerical aspects to substantiate the important effect of the upstream flow are implemented. Based on practical cases and laboratory works, upstream flow patterns for the Savonius rotor are divided into four types, namely uniform flow, guided flow, rotor wake flow and oscillating flow. Accordingly, conditions under which these upstream flow patterns arise are analyzed respectively. Experimental and numerical results are presented to clarify the influential factors underlying diverse upstream flow patterns. Furthermore, the relationship between the performance of the Savonius and the upstream flow is elucidated, facilitating the development of techniques of controlling the upstream flow. This review provides a systematic reference for the control of the upstream flow for the Savonius rotor, which has the tendency of developing into an independent technical branch.