During the last decade, relay networks have attracted a lot of interest due to their numerous benefits. The relaying technique allows extending the coverage zone of wireless networks and offers a higher reliability for communication systems. The performance of relay networks can be improved further by the use of automatic repeat request (ARQ) and hybrid automatic repeat request (HARQ) techniques. ARQ and HARQ are retransmission mechanisms that ensure a good quality of service even in absence of channel state information at the transmitter. We, firstly, study the spectral and energy efficiency of ARQ in Nakagami-m block-fading channels. We maximize both spectral efficiency and energy efficiency with respect to the transmitted power. We derive exact expressions as well as compact and tight approximation for the solutions of these problems. Our analysis shows that the two problems of maximizing spectral efficiency and energy efficiency with respect to the transmitted power are completely different and give different solutions. Additionally, operating with a power that maximizes energy efficiency can lead to a significant drop in the spectral efficiency, and vice versa. Next, we consider a three node relay network comprising a source, a relay, and a destination. The source transmits the message to the destination using HARQ with incremental redundancy (IR). The relay overhears the transmitted message, amplifies it using a variable gain amplifier, and then forwards the message to the destination. This latter combines both the source and the relay message and tries to decode the information. In case of decoding failure, the destination sends a negative acknowledgement. A new replica of the message containing new parity bits is then transmitted in the subsequent HARQ round. This process continues until successful decoding occurs at the destination or a maximum number M of rounds is reached. We study the performance of HARQ-IR over the considered relay channel from an information theoretic perspective. We derive exact expressions and bounds for the information outage probability, the average number of transmissions, and the average transmission rate. Moreover, we evaluate the delay experienced by Poisson arriving packets over the considered relay network. We also provide analytical expressions for the expected waiting time, the sojourn time, and the energy efficiency. The derived exact expressions are validated by Monte Carlo simulations. Finally, we consider a relay network consisting of a source, K relays, and a destination. The source transmits a message to the destination using HARQ-IR. We study the performance of HARQ-IR over dualhop multibranch amplify-and-forward relay channels. We derive exact expression for outage probability of the considered network. We investigate the benefit of relaying and the effect of changing the rate and the maximum number M of rounds on the outage probability.