With the development of high speed digital processor and solid state power electronics, more flexible waveforms become feasible to achieve by modern radar systems. In fact, the choice of waveforms has a significant impact on the performance of radar systems. In this paper, we review the conventional radar waveform design as well as explore the new generation of waveforms via different theoretical methods, including the most recent wavelet based waveforms. It is shown that the waveform design supports the radar advancement for more intelligent and divergent applications. In this endeavor, radar waveform design plays an even more important role in reaching specific purposes, in addition to range and speed detections, and further improves the performance and application scopes of radar systems.