The radio spectrum that can be used for wireless communications is a finite but extremely valuable resource. During the past two decades, with the proliferation of new wireless applications, the use of the radio spectrum has intensified to the point that improved spectrum sharing policies and new mechanisms are needed to enhance its utilization efficiency. This dissertation studies spectrum sharing and coexistence on both licensed and unlicensed bands for wireless networks. For licensed bands, we study two coexistence paradigms: transparent coexistence (a.k.a., underlay) and policy-based network cooperation (a.k.a., overlay). These two paradigms can offer significant improvement in spectrum utilization and throughput performance than the interweave paradigm. For unlicensed band, we study coexistence of Wi-Fi and LTE, the two most poplar wireless networks. / Ph. D.