Propagation characteristics of radio signals in the UHF band place fundamental limits on the design and performance of wireless personal communications systems, such as cellular mobile radio (CMR), wireless LAN's, and personal communication services (PCS). Because the radio link is direct to each subscriber, the prediction of signal characteristics is most important in urban areas where subscriber density is high, and the buildings have a profound influence on the propagation. This paper starts by reviewing the characteristic signal variations observed in CMR systems employing high base station antennas to cover macrocells having radius out to 20 km. Theoretical models incorporating diffraction are shown to explain the observed range dependence and shadow loss statistics. For the low base station antennas envisioned to cover microcells of radius out to 1 km for PCS applications, signal propagation is more strongly dependent on the building environment and on the location of the antennas in relation to the buildings. Various levels of theoretical modeling of this dependence are discussed in conjunction with measurements made in various building environments. Finally, the paper discusses recent advances in site specific prediction for outdoor and indoor propagation.