Since 1990s, the investigations of aerospace communication segment have not only been concerned with satellites, but increasingly with lower altitude repeaters flying in the stratosphere. They are the so-called high-altitude platforms (HAPs) with important advantages with respect to satellites in terms of reduced cost of implementation, deployment, and launch. However, HAPs are characterized by a reduced coverage, as compared with satellites. Nevertheless, in recent literature, HAPs are not regarded as competitors of the satellite technology. On the contrary, the emphasis is on the effective and seamless integration among heterogeneous aerospace segments (GEO, LEO, and HAP) and aerospace segments with terrestrial wireless networks in order to globally extend the broadband wireless connectivity. This paper is focused on the role of HAPs in providing global connectivity in future communication systems and services. Potentialities, enabling technologies, and challenges are presented from the perspective of the integrated terrestrial/HAPs/satellite communications infrastructure.