We consider network source coding for error-free networks with feedback from the sink nodes to the source nodes. We present several examples of networks with unlimited feedback to demonstrate that the presence of feedback strictly increases the set of achievable rate in both the lossy and lossless settings. We also observe that the presence of feedback can reduce the encoding and decoding complexity in some cases. Next, we derive general upper and lower bounds on the rate regions of networks with limited feedback demonstrating a fundamental tradeoff between the forward rate and the feedback rate. Finally we restrict our attention to zero error source coding with limited feedback and decoder side information and derive the exact tradeoff between the forward rate and the feedback rate for several classes of sources. A surprising result is that even a zero rate feedback can reduce the optimal forward rate by an arbitrary factor.