Hybrid terrestrial-satellite transmission systems have been among hottest spots in the wireless communication industry due to the high demand for global high data rates. In such systems, free-space optical (FSO) technology is advocated for assessing the feeder links (ground-satellite) in order to fulfill high data rates requirements and provide a larger coverage in terms of the connected number of users. This paper gives an overview of various components of very-high throughput hybrid terrestrial-satellite communication system with an FSO feeder link, and Ka-band multibeam RF channels for the satellite ground link. In this survey paper, we depict the main communication challenges in the FSO side such as pointing error, turbulence, cloud blockage, and also the multibeam RF side such as spectrum scarcity, inter-beam interference, and security. Based on these challenges we point out some potential research directions.