We consider a general model of non-Bayesian social learning. A network of agents observe signals about an underlying fundamental parameter. At each period, every agent solves a non-parametric estimation problem using her previous information and the most recent estimates of her neighbors. Agents are uncertain about the distribution of signals as well as the exact network structure and therefore appeal to a robust estimation procedure. We first characterize the functional properties of the resulting robust opinion aggregators. These aggregators admit the linear DeGroot model as a particular parametric specification. However, robust opinion aggregators allow for several economically relevant patterns ruled out by the linear model. For instance, agents can feature dislike (or attraction) for extreme opinions, confirmatory bias, as well as discard information obtained from sources perceived as redundant. We then show that under this general model it is still possible to link the long-run behavior of the opinions (e.g. convergence, speed of learning and consensus) to the structure of the underlying network. In particular, we provide sufficient conditions for convergence, consensus and for bounds on the speed of convergence. Finally, we study the Wisdom of the Crowd (Golub and Jackson, 2010) in our environment.