The classical framework on distributed inference considers a set of nodes taking measurements and a fusion center making the final decision on the underlying phenomenon, without dealing with the issue of transporting the measurements to the fusion center. Such an approach introduces significant overhead in communication. Communicating all the raw data for inference is not scalable: in this case, the per-node average energy consumption and the total bandwidth requirement become unbounded as the network grows. We design scalable algorithms for two scenarios with guarantees for inference whose communication requirements and complexity are bounded even as the network grows. This is achieved through distributed computation of a sufficient statistic, which results in reduction of data dimensionality while ensuring no loss in inference accuracy at the fusion center. The first scenario deals with multihop routing and fusion of spatially correlated measurements, incorporated through a Markov random field model. The second scenario deals with design of medium-access control (MAC) with the aim of computing a sufficient statistic for inference over a multiple access channel.