This paper studies a novel mobile relaying technique, where relays of high mobility are employed to assist the communications from source to destination. By exploiting the predictable channel variations introduced by relay mobility, we study the throughput maximization problem in a mobile relaying system via dynamic rate and power allocations at the source and relay. An optimization problem is formulated for a finite time horizon, subject to an information-causality constraint, which results from the data buffering employed at the relay. It is found that the optimal power allocations across the different time slots follow a "stair-case" water filling (WF) structure, with non-increasing and non-decreasing water levels at the source and relay, respectively. For the special case where the relay moves unidirectionally from source to destination, the optimal power allocations reduce to the conventional WF with constant water levels. Numerical results show that with appropriate trajectory design, mobile relaying is able to achieve tremendous throughput gain over the conventional static relaying.