Dynamic spectrum sharing (DSS) has recently attracted keen interest from regulatory bodies around the world as a key strategy to overcome spectrum scarcity in beyond 5G networks. In the United States, the Federal Communications Commission has adopted a three-tier DSS model for the Citizens Broadband Radio Service (CBRS) band managed by a spectrum access system (SAS) to share incumbents' spectrum with commercial cellular broadband applications. In this article, we first present a survey of current DSS approaches and their limitations and then discuss the benefits of using in-band full-duplex (IBFD) techniques in DSS networks. To illustrate the improvement in the performance of priority access license (PAL) and general authorized access (GAA) users in an IBFD-assisted CBRS, we consider a CBRS mobile broadband network (MBN) architecture comprising an incumbent in the form of a MIMO radar system and an IBFD MIMO MBN, consisting of PAL and GAA users. In particular, we design joint beamformers at the MBN, with constraints on transmit power at the MBN and detection probability of the radar system, and beamformers at the radar system to mitigate the interference from the radar system toward the cellular system. It is shown that the IBFD CBRS network architecture not only leads to improved performance of PAL and GAA users, but does so while producing less interference toward the radar than state-of-the-art half-duplex solutions. Finally, we present some open research challenges to invigorate research on beyond 5G IBFD DSS networks.