This Springerbreif introduces a threshold-based channel sparsification approach, and then, the sparsity is exploited for scalable channel training. Last but not least, this brief introduces two scalable cooperative signal detection algorithms in C-RANs. The authors wish to spur new research activities in the following important question: how to leverage the revolutionary architecture of C-RAN to attain unprecedented system capacity at an affordable cost and complexity. Cloud radio access network (C-RAN) is a novel mobile network architecture that has a lot of significance in future wireless networks like 5G. the high density of remote radio heads in C-RANs leads to severe scalability issues in terms of computational and implementation complexities. This Springerbrief undertakes a comprehensive study on scalable signal processing for C-RANs, where 'scalable' means that the computational and implementation complexities do not grow rapidly with the network size. This Springerbrief will be target researchers and professionals working in the Cloud Radio Access Network (C-Ran) field, as well as advanced-level students studying electrical engineering.