Research on the wisdom of crowds is motivated by the observation that the average belief in a large group can be accurate even when group members are individually inaccurate. A common theoretical assumption in previous research is that accurate group beliefs can emerge only when group members are statistically independent. However, network models of belief formation suggest that the effect of social influence depends on the structure of social networks. We present a theoretical overview and two experimental studies showing that, under the right conditions, social influence can improve the accuracy of both individual group members and the group as a whole. The results support the argument that interacting groups can produce collective intelligence that surpasses the collected intelligence of independent individuals.