In cloud radio access networks (C-RANs), the baseband processing of the radio units (RUs) is migrated to remote control units (CUs). This is made possible by a network of backhaul links that connects RUs and CUs and that carries compressed baseband signals. While prior work has focused mostly on single-hop backhaul networks, this paper investigates efficient backhaul compression strategies for the uplink of C-RANs with a general multihop backhaul topology. A baseline multiplex-and-forward (MF) scheme is first studied in which each RU forwards the bit streams received from the connected RUs without any processing. It is observed that this strategy may cause significant performance degradation in the presence of a dense deployment of RUs with a well connected backhaul network. To obviate this problem, a scheme is proposed in which each RU decompresses the received bit streams and performs linear in-network processing of the decompressed signals. For both the MF and the decompress-process-and-recompress (DPR) backhaul schemes, the optimal design is addressed with the aim of maximizing the sum-rate under the backhaul capacity constraints. Recognizing the significant demands of the optimal solution of the DPR scheme in terms of channel state information (CSI) at the RUs, decentralized optimization algorithms are proposed under the assumption of limited CSI at the RUs. Numerical results are provided to compare the performance of the MF and DPR schemes, highlighting the potential advantage of in-network processing and the impact of CSI limitations.