Next-generation of satellite communication (SatCom) networks are expected to support extremely high data rates for a seamless integration into future large satellite-terrestrial networks. In view of the coming spectral limitations, the main challenge is to reduce the cost (satellite launch and operation) per bit, which can be achieved by enhancing the spectral efficiencies. In addition, the capability to quickly and flexibly assign radio resources according to the traffic demand distribution has become a must for future multibeam broadband satellite systems. This letter presents the radio resource management problems encountered in the design of future broadband SatComs and provides a comprehensive overview of the available techniques to address such challenges. Firstly, we focus on the demand-matching formulation of the power and bandwidth assignment. Secondly, we present the scheduling design in practical multibeam satellite systems. Finally, a number of future challenges and the respective open research topics are described.