Increased amounts of bandwidth are required to guarantee both high-quality/high-rate wireless services (4G and 5G) and reliable sensing capabilities such as automotive radar, air traffic control, earth geophysical monitoring and security applications. Therefore, co-existence between radar and communication systems using overlapping bandwidths has been a primary investigation field in recent years. Various signal processing techniques such as interference mitigation, pre-coding or spatial separation, and waveform design allow both radar and communications to share the spectrum. This article reviews recent work on co-existence between radar and communication systems, including signal models, waveform design and signal processing techniques. Our goal is to survey contributions in this area in order to provide a primary starting point for new researchers interested in these problems.