Understanding information exchange and aggregation on networks is a central problem in theoretical economics, probability and statistics. We study a standard model of economic agents on the nodes of a social network graph who learn a binary “state of the world” S, from initial signals, by repeatedly observing each other’s best guesses. Asymptotic learning is said to occur on a family of graphs Gn = (Vn, En) with |Vn| → ∞ if with probability tending to 1 as n → ∞ all agents in Gn eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.