With the recent commercialization of 5G and initiation of 6G research, satellite communication technology that can provide high-speed Internet services all around the Earth is actively being studied. The 3rd Generation Partnership Project (3GPP) has initiated 5G New Radio (NR) based non-terrestrial network (NTN) research to extend traditional cellular network-based service coverage. NTN is expected to provide ubiquitous services to areas such as mountains and oceans where 5G terrestrial networks cannot be covered. Toward this end, the satellite communication technology should be developed with the consideration of the long propagation delay, large Doppler effect, and large satellite beam coverage, which are not typically considered in 5G NR terrestrial networks. In this paper, we summarize and analyze the channel modeling and features for NTN including satellites, unmanned aerial systems of the 3GPP NR technical report, focusing on low Earth orbit (LEO) satellite communication channels with lower delay characteristics compared to geostationary (GEO) satellites. Furthermore, we discuss new research trends and open challenges of LEO satellite communication systems based on the described channel characterization and modeling.