Connectivity in rural areas is one of the main challenges of communication networks. To overcome this challenge, a variety of solutions for different situations are required. Optimizing the current networking paradigms is therefore mandatory. The high costs of infrastructure and the low revenue of cell sites in rural areas compared with urban areas are especially unattractive for telecommunication operators. Therefore, space, air, and ground networks should all be optimized for achieving connectivity in rural areas. We highlight the latest works on rural connectivity, discuss the solutions for terrestrial networks, and study the potential benefits of nonterrestrial networks. Furthermore, we present an overview of artificial intelligence (AI) techniques for improving space, air, and ground networks, hence improving connectivity in rural areas. AI enables intelligent communications and can integrate space, air, and ground networks for rural connectivity. We discuss the rural connectivity challenges and highlight the latest projects and research and the empowerment of networks using AI. Finally, we discuss the potential positive impacts of providing connectivity to rural communities.