Free-space optical (FSO) communications have gained significant interest over the last few years, thanks to the capability to transport extremely high-speed data over long distances without exhausting radio frequency (RF) resources. FSO communication is widely considered in various network scenarios, such as inter-satellite/deep-space links, ground-station/vehicles, satellite/aerial links, or terrestrial links. It is expected to be a key enabling technology for the next generation of 6G wireless networks. Nevertheless, despite the great potential of FSO communications, its performance suffers from various limitations and challenges: atmospheric turbulence, clouds, weather conditions, and pointing misalignment. The error-control solutions, including physical layer (PHY) and link-layer methods, aim to mitigate the transmission errors caused by such adverse issues. While the existing surveys on error-control solutions in FSO systems primarily focussed on the PHY methods, we instead provide a review of link-layer solutions. In particular, we conduct an extensive literature survey of state-of-the-art retransmission protocols, both automatic repeat request (ARQ) and hybrid ARQ (HARQ), for various FSO communication scenarios, including point-to-point terrestrial, cooperative, multi-hop relaying, hybrid FSO/RF, satellite/aerial, and deep-space systems. Furthermore, we provide a survey of recent literature and insightful discussion on the cross-layer design frameworks related to link-layer retransmission protocols in FSO communication networks. Finally, the lessons learned, design guidelines, related open issues, and future research directions are exposed.