This article aims to provide a comprehensive overview for key issues in broadband LEO satellite communication systems. First of all, the network architecture is introduced, which is the basis of the whole system. The space-based LEO system with ISL, which requires a small number of ground gateways, is the focus. In this system, the satellite constellation design is important with impact on key system performances such as coverage. Two popular LEO constellations, the walker Delta and Star constellations, are introduced. Given satellite constellations, proper beam coverage schemes should be employed at satellites to provide seamless coverage all over the world. A hybrid wide and spot beam coverage scheme is presented, where the LEO provides a wide beam for large area coverage and several steering spot beams for highspeed data access. Moreover, special coverage schemes should be designed in broadband LEO systems for the interference coordination between LEO and GEO. To protect GEO communications, LEO satellites should be turned off if they cause interference to GEO. In this case, to provide services for users covered by the turned-off LEO satellites, a progressive pitch method and a coverage expanding method can be employed. Finally, the coverage performance of LEO is also closely related to resource management schemes. The global resource management for broadband LEO systems is complicated, involving a large amount of data, and a two-level management structure should be employed. Using this structure, an NMC with powerful storage and processing capabilities is employed to carry out the first-level management, making strategies based on all information collected from the whole system. Then satellite base stations with limited capabilities are employed to respond to the strategies generated by NMC in real time.