The low-Earth orbiting (LEO) satellite constellations in the 90s (such as Iridium and Globalstar), although representing a major technical breakthrough, were not able to achieve the initial goal of complementing the second-generation mobile terrestrial networks due to the rapid worldwide adoption of GSM and other standards. However, the decline of conventional linear television and the persisting need to mitigate the digital divide still affecting billions of people recently generated a renewed interest by private investors for Low-Earth Orbiting (LEO) satellite mega-constellations. The mega-constellations under deployment can provide lower delays versus geostationary (GEO) satellites, broadband access anywhere, anytime leveraging the low-cost series production of small satellites, and more affordable launch solutions. At the end of the last decade, key industrial players realized the potential complementary role satellites can play to extend the 5G terrestrial network coverage over low-density populated areas, oceans, or similar. This has led to great technological developments and a sharp reduction in LEO satellite volume, weight, and, ultimately, manufacturing and launching costs. Also, it has triggered the inclusion of a non terrestrial network (NTN) component in the latest 5G 3GPP standard releases. Yet, there are many technological challenges remaining to ensure that both the quality and cost of the NTN services are comparable to the terrestrial counterpart. This is mainly due to the constraints in satellite payload power, mass, and antenna size. This comes in addition to the stringent power flux density limitations on the ground, in particular in the below 6 GHz satellite bands. The required order of magnitude increase of the effective delivered throughput and service cost reduction can only be achieved by a mix of system architectures and innovative technologies for both the space and ground segments. Space communication systems and technologies will also play a key role in human return to the Moon planned for mid-2020, to prepare for human exploration of Mars in the more distant future and further cosmic exploration. As missions voyage further from Earth, it is important to consider how we can continue to reliably communicate with them and how they will accurately navigate through space when they are so far from home.