Extension of usable frequency spectrum from microwave to millimeter-wave (mmWave) is one of the key research directions in addressing the capacity demands of emerging 5th-generation communication networks. This paper presents a thorough analysis on the azimuthal multipath shape factors and second-order fading statistics (SOFS) of outdoor and indoor mmWave radio propagation channels. The well-established analytical relationship of plain angular statistics of a radio propagation channel with the channel’s fading statistics is used to study the channel’s fading characteristics. The plain angle-of-arrival measurement results available in the open literature for four different outdoor radio propagation scenarios at 38 GHz, as well as nine different indoor radio propagation scenarios at 28 GHz and 38 GHz bands, are extracted by using different graphical data interpretation techniques. The considered quantifiers for energy dispersion in angular domain and SOFS are true standard-deviation, angular spread, angular constriction, and direction of maximum fading; and spatial coherence distance, spatial auto-covariance, average fade duration, and level-crossing-rate; respectively. This study focuses on the angular spread analysis only in the azimuth plane. The conducted analysis on angular spread and SOFS is of high significance in designing modulation schemes, equalization schemes, antenna-beams, channel estimation, error-correction techniques, and interleaving algorithms; for mmWave outdoor and indoor radio propagation environments.