We describe and discuss some of the current challenges facing radar that result from continued spectral encroachment, which necessitating enhanced robustness to interference, agile waveform-diverse operation, and greater synergy between the signal processing and the physical radar/environment. Subsequently, specific research topics are suggested in which spectrum engineering and waveform diversity may yield viable solutions. In so doing, this paper also provides an introduction to the special session on radar spectrum engineering and waveform diversity affiliated with NATO Task Groups SET-182 and SET-179, respectively.I.