This paper provides an up-to-date review of wireless communications service provisioning in rural or remote areas from High-Altitude Platforms (HAPs) exploiting cellular radio spectrum. With the recent International Telecommunication Union (ITU) report showing that as much as 74% of the population in Africa, most of which are living in rural areas, do not have access to broadband, this paper focuses on the potential of using HAPs as an alternative to terrestrial systems for wireless communication in rural communities. Considering the typically low user densities in rural areas and the importance of HAP coverage maximization while ensuring harmless coexistence with terrestrial systems in rural areas, this paper explores extending the achievable wireless coverage from a HAP. This takes into consideration the coexistence of a HAP with terrestrial systems using intelligent techniques to dynamically manage radio resources and mitigate interference. Studies have shown that efficient intelligent radio resource and topology management can minimize inter-system interference and ensure coexistence with improved system performance. Potential techniques for coverage extension such as exploiting the spatial characteristics of array antennas, radio environment maps (REMs) and deviceto-device (D2D) communications are discussed. Generally, this paper presents a comprehensive review of significant HAP related studies and their outcomes.