This dissertation investigates covert communication in dynamic wireless communication environments. A key goal is to provide insight about the capabilities of a transmitter desiring to remain covert and analogously, the capabilities of the party attempting to detect covert communications. The first chapter provides background on covert communications prior to this work. The second chapter studies the theoretical limits of covert communication and proves that positive rate is achievable when a jammer is added to the classical Alice/Bob/Warden Willie model. The third chapter expands on the second chapter by considering more generally the impact of the dynamics of the environment on the Alice/Bob/Warden Willie model. The dynamics of the environment generate uncertainty at Willie even if the jammer does not vary his/her power or even if Willie employs an antenna array to mitigate the jamming. The fourth and fifth chapters investigate the impact of considering the exact continuous-time model rather than a discrete-time model approximation. In particular, detectors at Willie which leverage information in the continuous-time domain outperform detectors based on the discrete-time model approximation. The fourth and fifth chapters consider the continuous-time model of the Alice/Bob/Willie scenario and the Alice/Bob/Willie/Jammer scenarios respectively. The fourth and fifth chapters may appear to question the results of Chapter 2, Chapter 3 and prior wireless covert communication related research. However, these final chapters provide insight about different detectors available to Willie and the importance of Alice implementing communication schemes which do not contain features that significantly differ from Willie\u27s observation under the null hypothesis. Our work has demonstrated how the covert throughput critically depends on Willie\u27s knowledge of the environment and how the covert transmitter, allies in the area, or the dynamics of the environment itself might impact that knowledge. Future work will continue to move covert communications closer to practice by integrating further aspects of practical communication system design
