Millimeter-wave (mm-wave) radio is attracting attention as one of the key enabling physical layer technologies for the fifth-generation (5G) mobile access and backhaul. This paper aims at clarifying possible roles of mm-wave radio in the 5G development and performing a comprehensive literature survey on mm-wave radio channel modeling essential for the feasibility study. Emphasis in the literature survey is laid on grasping the typical behavior of mm-wave channels, identifying missing features in the presently available channel models for the design and evaluation of the mm-wave radio links within the 5G context, and exemplifying different channel modeling activities through analyses performed in the authors' group. As a key technological element of the mm-wave radios, reduced complexity beamforming is also addressed. Design criteria of the beamforming are developed based on the spatial multipath characteristics of measured indoor mm-wave channels.