Wireless data transmission suffers from the fading nature of wireless channels, where the instantaneous channel conditions and hence transmission rates randomly fluctuate over time. Consequently, data arrivals at each transmitter might not be transmitted instantly. To cope with this situation, the transmitter employs buffer to store the data temporarily for later transmission. While data buffering enables more efficient radio resource allocation to opportunistically select the favorable fading conditions for transmission, it introduces queuing delay that needs to be controlled in order to meet the end-to-end delay quality-ofservice (QoS) requirements in supporting delay-sensitive communications. In this thesis, we study and develop radio resource allocation schemes for buffer-aided communications over wireless fading channels under statistical delay constraints. Using the buffering capability as a means to exploit the fading diversity, the nodes (source and relay) perform resource allocation, and adapt their transmissions to the channel state information (CSI) in order to enhance the system throughput while maintaining the statistical delay QoS requirements in terms of upper-bounded average delay or delay-outage probability.The thesis starts by considering a source-destination communications link over a fading channel with data arriving at the source transmission buffer. In the first scenario, the source is assumed to have a maximum power constraint and an average delay constraint. We consider admission control applied on random data arrivals to the source buffer in order to avoid constraint violation, and study the joint optimal data admission control and power allocation (AC-PA) problem for throughput maximization. In the second scenario, we consider an energy-harvesting (EH) source, where random amounts of energy are harvested from renewable energy sources, and stored in a battery during the course of data transmission. In every transmission time slot, the source is constrained to use at most the amount of energy currently stored. We then explore optimal power allocation problems for such EH systems under average delay or delay-outage constraints. We formulate the problems as infinite horizon constrained Markov decision process (MDP) problems, which incorporate the random variations of the fading channel, data arrival, and EH processes. A novel solution approach based on post-decision state-value function is proposed to study the properties of the optimal solutions. We also propose online allocation algorithms when the statistical knowledge of the random processes is unknown, which is typical in real-life communications. Illustrative results demonstrate the effectiveness of the proposed algorithms over existing approaches iii under similar power and delay constraints.The thesis continues with a source-relay-destination communications link over fading channels with buffers available at both source and relay, as part of a multi-hop network. We investigate and develop optimal resource allocation schemes ...