The fifth‐generation (5G) mobile communication systems require high spectrum efficiency due to the explosive increase of data traffic and green networking requirement. The demand for higher spectrum and energy efficiency has driven system designers to exploit more spatial degrees of both the elevation and azimuth domains through the use of large‐scale antenna systems with two or three‐dimensional (3D) array structures. The performance of full‐dimensional multiple‐input‐multiple‐output (FD‐MIMO) depends critically on both the space–time transmission schemes and 3D channel propagation characteristics. Therefore, it is important to understand and describe the 3D spatial propagation of signals in multipath radio channels. This article aims to provide a comprehensive introduction to the fundamental concept and approaches characterizing and modeling the 3D spatial channels. We first present the bi‐directional space‐time scattering models of multipath channels and the polarized multipath components (MPCs). We then briefly introduce the development of 3D channel modeling and the main projects and standards in the industrial community. Finally, we summarize and discuss the current 3D channel models based on extensive field measurement for various cellular network scenarios, such as outdoor, indoor, outdoor‐to‐indoor (O2I), and vehicular communication scenarios.