Since the early 1990s, a large number of chaos-based communication systems have been proposed exploiting the properties of chaotic waveforms. The motivation lies in the significant advantages provided by this class of non-linear signals. For this aim, many communication schemes and applications have been specially designed for chaos-based communication systems where energy, data rate, and synchronization awareness are considered in most designs. Recently, the major focus, however, has been given to the non-coherent chaos-based systems to benefit from the advantages of chaotic signals and noncoherent detection and to avoid the use of chaotic synchronization, which suffers from weak performance in the presence of additive noise. This paper presents a comprehensive survey of the entire wireless radio frequency chaos-based communication systems. First, it outlines the challenges of chaos implementations and synchronization methods, followed by comprehensive literature review and analysis of chaos-based coherent techniques and their applications. In the second part of the survey, we offer a taxonomy of the current literature by focusing on non-coherent detection methods. For each modulation class, this paper categorizes different transmission techniques by elaborating on its modulation, receiver type, data rate, complexity, energy efficiency, multiple access scheme, and performance. In addition, this survey reports on the analysis of tradeoff between different chaos-based communication systems. Finally, several concluding remarks are discussed.