Fifth generation (5G), beyond 5G (B5G), and future sixth generation (6G) mobile networks are foreseen to increasingly account for heterogeneous networks toward ubiquitous communications with non-terrestrial networks (NTNs). Furthermore, in 5G mobile networks, massive machine type communications has been introduced for Internet of Things (IoT) applications aiming at low energy consumption, low to medium data rates, burst transmissions, and massive connectivity. It is expected that IoT communications will take an even larger portion in B5G and 6G mobile networks. Robust communications in such high-mobility NTN deployments including unmanned aerial vehicles (UAVs), airborne platforms, and satellite systems, need novel modulation waveforms that can deal with the induced severe Doppler effects. Orthogonal time frequency space (OTFS) modulation has gained tremendous interest in recent years as an effective technology for coping with high Doppler channels. OTFS essentially transforms a time-varying fading channel into a quasi-static channel in the delay-Doppler domain. In this paper, for the first time, an overview on OTFS modulation for NTNs is provided including basic concepts and applications in UAVs, airborne networks, and satellite systems. A case study related to an application in high Doppler airborne communication networks is also provided to illustrate the potential of OTFS modulation in providing robust transmission links in high-mobility scenarios. This survey will be helpful for researchers and practitioners to keep abreast about the potential of OTFS modulation in NTNs. © 2023 IEEE.