Many organizations recognize non-terrestrial networks (NTNs) as a key component to provide cost-effective and high-capacity connectivity in future 6th generation (6G) wireless networks. Despite this premise, there are still many questions to be answered for proper network design, including those associated to latency and coverage constraints. In this paper, after reviewing research activities on NTNs, we present the characteristics and enabling technologies of NTNs in the 6G landscape and shed light on the challenges in the field that are still open for future research. As a case study, we evaluate the performance of an NTN scenario in which aerial/space vehicles use millimeter wave (mmWave) frequencies to provide access connectivity to on-the-ground mobile terminals as a function of different networking configurations.