As compared to terrestrial systems, the design of Satellite Communication (SatCom) systems require a different approach due to differences in terms of wave propagation, operating frequency, antenna structures, interfering sources, limitations of onboard processing, power limitations and transceiver impairments. In this regard, this letter aims to identify and discuss important modeling and design aspects of the next generation High Throughput Satellite (HTS) systems. First, communication models of HTSs including the ones for multibeam and multicarrier satellites, multiple antenna techniques, and for SatCom payloads and antennas are highlighted and discussed. Subsequently, various design aspects of SatCom transceivers including impairments related to the transceiver, payload and channel, and traffic-based coverage adaptation are presented. Finally, some open topics for the design of next generation HTSs are identified and discussed.