Seamless and ubiquitous coverage are key factors for future cellular networks. Despite capacity and data rates being the main topics under discussion when envisioning the Fifth Generation (5G) and beyond of mobile communications, network coverage remains one of the major issues since coverage quality highly impacts the system performance and end-user experience. The increasing number of base stations and user terminals is anticipated to negatively impact the network coverage due to increasing interference. Furthermore, the "ubiquitous coverage" use cases, including rural and isolated areas, present a significant challenge for mobile communication technologies. This survey presents an overview of the concept of coverage, highlighting the ways it is studied, measured, and how it impacts the network performance. Additionally, an overlook of the most important key performance indicators influenced by coverage, which may affect the envisioned use cases with respect to throughput, latency, and massive connectivity, are discussed. Moreover, the main existing developments and deployments which are expected to augment the network coverage, in order to meet the requirements of the emerging systems, are presented as well as implementation challenges.