Radar performance is strongly dependent on the transmitted waveform and its parameters which must be adapted to the surrounding environment, radar mission, goal, and task. Waveform diversity is a relatively new paradigm involving a continuous variation and adaptation of the transmitted signal to dynamically optimize the radar performance and fulfill the more and more stressing requirements. In this context, cognitive radar waveform design in spectrally dense environments is a very challenging and topical problem. This paper deals with the synthesis of signals optimizing radar capabilities while satisfying spectral compatibility constraints. Specifically, the design of radar waveforms, sharing appealing features and ensuring spectral coexistence with other Radio Frequency (RF) systems, is introduced and discussed according to a rigorous framework.