This paper provides an analysis of radio wave scattering for frequencies ranging from the microwave to the Terahertz band (e.g., 1 GHz - 1 THz), by studying the scattering power reradiated from various types of materials with different surface roughnesses. First, fundamentals of scattering and reflection are developed and explained for use in wireless mobile radio, and the effect of scattering on the reflection coefficient for rough surfaces is investigated. Received power is derived using two popular scattering models - the directive scattering (DS) model and the radar cross section (RCS) model through simulations over a wide range of frequencies, materials, and orientations for the two models, and measurements confirm the accuracy of the DS model at 140 GHz. This paper shows that scattering can become a prominent propagation mechanism as frequencies extend to millimeter-wave (mmWave) and beyond, but at other times can be treated like simple reflection. Knowledge of scattering effects is critical for appropriate and realistic channel models, which further support the development of massive multiple input-multiple output (MIMO) techniques, localization, ray tracing tool design, and imaging for future 5G and 6G wireless systems.