Opportunistic spectrum sharing (OSS) and cooperative spectrum sharing (CSS) are typical dynamic spectrum accessing (DSA) technologies to effectively improve spectrum efficiency (SE) and energy efficiency (EE). However, OSS provides no benefit to the primary user, whereas CSS, although simultaneously improving SE of the primary user and the secondary user, needs a proper cooperative mechanism with negotiation cost. To overcome these drawbacks, two kinds of relay OSS (ROSS) models are proposed to maximize SE and EE, respectively. When full-duplex transceiver is adopted by the secondary user, the proposed ROSS models can simultaneously improve the performance of both the primary user and the secondary user without requiring any negotiation. To make the study more complete, we consider both perfect channel state information (CSI) and imperfect CSI scenarios. Numerical results demonstrate the effectiveness of the proposed models and show that the performance of both the primary user and the secondary user can be improved under ROSS models.