This paper introduces a general approach to modeling boundedly rational observational learning in dynamic environments of decision making under uncertainty. Quasi-Bayesian updating reduces the complexity of fully rational inferences from observed actions by treating each observed action as if it were based only on the initial private information of the respective decision maker. We conduct a laboratory experiment of observational learning in a social network and find strong evidence for Quasi-Bayesian updating. Further, we consider a general model of repeated interaction in social networks with binary actions, and provide a characterization of the informational environment such that consensus occurs in any strongly connected network structure, under Quasi-Bayesian updating functions. Finally, we show that asymptotic learning fails as the size of the network grows to infinity.