Automatic repeat request (ARQ) schemes, and in particular hybrid-ARQ (HARQ) schemes, which jointly adopt forward error correction (FEC) and ARQ, are essential to provide reliable data transmission in wireless communications systems. However, the feedback from the receiver to the transmitter and the retransmission process used in ARQ incurs significant cost in terms of power efficiency, throughput, computational power and delay. Unfortunately, such drawbacks can limit their applications to several current and emerging technologies. More specifically, the increasing number of wireless users has create spectrum scarcity, relying on small-size batteries create power constraints, deployment of real-time applications boost the demand for ultralow delay networks, and the ultra-small low-cost internet of things (IoT) devices has limited signal processing and computation capabilities. Consequently, extensive research efforts have been dedicated to overcome the limitations inherent in HARQ. This survey paper provides an extensive literature review of the state-of-the-art HARQ techniques and discusses their integration in various wireless technologies. Moreover, it provides insights on advantages and disadvantages of particular ARQ types and discusses open problems and future directions.