Although in cellular networks full duplex and dynamic time-division duplexing promise increased spectrum efficiency, their potential is so far challenged by increased interference. While previous studies have shown that self-interference can be suppressed to a sufficient level, we show that the cross-link interference for both duplexing modes, especially from base station to base station, is the remaining challenge in multi-cell networks, restricting the uplink performance. Using beamforming techniques of low complexity, we show that this interference can be mitigated, and that full duplex and dynamic time-division duplexing can substantially increase the capacity of multi-cell networks. Our results suggest that if we can control the cross-link interference in full duplex, we can almost double the multi-cell network capacity as well as user throughput. Therefore, the techniques in this article have the potential to enable a smooth introduction of full duplex into cellular systems.