Book excerpt: The Arbitrarily Varying Channel (AVC) can be interpreted as a model of a channel jammed by an intelligent and unpredictable adversary. In this report, we investigate the asymptotic reliability of optimum random block codes on Gaussian Arbitrarily Varying Channels (GAVCs). A GAVC is a discrete-time, memoryless Gaussian channel with input power Pt and noise power Ne, which is further corrupted by an additive jamming signal. The statistics of this signal are unknown and may be arbitrary, except that they are subject to a power constraint Pj. We distinguish between two types of power constraints: peak and average. For peak constraints on the input power and the jamming power, we show that the GAVC has a (strong) capacity. For the remaining cases, in which the transmitter and/or the jammer are subject to average power constraints, only lambda-capacities are found. The asymptotic error probabilities suffered by optimal random codes in these cases are determined. Our results suggest that if the jammer is subject only to an average power constraint, reliable communication is impossible at any positive code rate.