In this talk we describe two models of collective inference. The first, based on joint work with Alexandre Proutière and Mesrob Ohanessian, deals with categorization of a "news item" based on the reaction of readers exposed sequentially. We propose policies for choosing who to expose based on previous reactions, which achieve a desirable trade-off between "spamming", ie exposure of uninterested readers, and "missed opportunity", ie non-exposure of interested readers. The second model, based on joint work with Kuang Xu, is motivated by crowdsourcing. It features experts with distinct abilities and limited processing power, and inference tasks that consist in labelling an input with some prescribed confidence level based on noisy expert feedback. Policies are described which maximize the load of jobs the system can correctly handle in an asymptotic regime of high confidence level target.