This chapter focuses on aerial channelpropagation modeling and waveform design for wireless networks with UAVs. We begin by introducing the fundamentals of radio wave propagation and modeling, and, then, we provide an overview of the salient characteristics of aerial wireless channels for UAVs, with a focus on how they differ from the more familiar and well-studied terrestrial wireless channels. Next we characterize large-scale propagation channel effects, including path loss, shadowing, LOS probability, and atmospheric and weather effects, and we discuss the use of ray tracing for UAV channel modelling. We also discuss various small-scale propagation effects. We then turn our attention to waveform design, by reviewing the needed background and providing a small set of exemplary waveforms that showcase the main waveform design considerations for UAV wireless communications and networking.