To help meet the growing demand for wireless data capacity, the United States Federal Communications Commission (FCC) and National Telecommunications and Information Administration (NTIA) define and regulate a spectrum-sharing approach in several radio frequency (RF) bands, with sharing in additional bands expected in the near future. This paper examines the case in which some of the users in the shared bands are government radars, as is the case in the 3.5 GHz Citizens Broadband Radio Service (CBRS) band. This paper surveys topics related to dynamic spectrum sharing (DSS) of RF bands between government radars and communication systems, including spectrum policy, dynamic spectrum access (DSA), dynamic frequency selection (DFS) and frequency assignment, Primary User (PU) protection and privacy, radar-communications interference mitigation, and joint radar-communications system design. The purpose of this paper is to provide readers with a summary of current knowledge of these aforementioned concepts while also providing references so that topics of interest may be studied deeper. The structure of this paper is broken into several topics, where within each topic table(s) provide a survey of the relevant topic. The contribution made includes over 200 references. Tables include summaries of approaches described in multiple references, as well as descriptions and summaries of individual references used throughout the survey. A taxonomy of approaches applicable to spectrum sharing between radar and communication systems is provided, as are conclusions and recommendations. Findings include existing technology, systems, and regulations utilizing the CBRS in its current structure. Therefore, all of the advancements will most likely be derived using a combination, derivative, or adapted methodology defined in the different sections throughout this survey.