Inspired by the success of multi-carrier waveforms such as Orthogonal Frequency Division Multiplexing (OFDM) in radio communication, multi-carrier based radar waveform designs have gained strong interest recently. Reasons for this include their resistance to multipath fading, ability to overcome the limitations of a congested frequency spectrum, ability to exploit frequency diversity gains, and potential to perform radar and communication functions simultaneously within the same hardware using the same waveform. This paper provides recent research on multi-carrier waveform design for joint radar and communication systems. First, we employ OFDM to modulate Multi-Frequency Complementary Phase Coded (MCPC) sequences in order to improve radar range resolution performance. Next, it is shown that even though these MCPC sequences produce periodic autocorrelation sidelobes with deep nulls, their overall sidelobe level is higher than that of other traditional pulse-compression radar waveforms such as Linear Frequency Modulated (LFM) waveforms. A method, termed Polar Signal Detection, is introduced as a means of overcoming these large autocorrelation sidelobes without sacrificing range measurement resolution.