In the 1970's and 1980's, we saw phenomenal advancement in nonlinear sci ence, which had led to many important discoveries that greatly improve our understanding of the physical world. Among them, the discovery of chaos in deterministic systems is unarguably one of the most revolutionary scientific findings. We are now able to explain the apparent complexity and subtle or der exhibited by many physical systems under the unified framework of chaos theory. The past decade has seen heightened interest in the exploitation of chaos for useful applications in engineering systems. One application area that has attracted a great deal of attention is communications. Chaotic signals, by virtue of their wide band characteristic, are natural candidates for carrying information in a spread-spectrum communication environment. The use of chaotic signals in communications thus naturally inherits the advantages that are currently being offered by conventional spread-spectrum communication systems, such as robustness in multi path environments, resistance to jam ming, low probability of interception, etc. In addition, chaotic signals are easy to generate and hence offer a potentially low-cost solution to spread spectrum communications. Although many practical problems need to be solved before chaos-based communications can be realized in practice, the field has advanced rapidly during the past few years and it now reaches a point where abstract concepts from physics and mathematics have been fruitfully ported to techniques that allow information to be carried by chaotic signals.