Thanks to the availability of user profiles and records of activity, online social network analysis can discover complex individual and social behavior patterns. The emergence of trust between users of online services is one of the most important phenomena, but it's also hard to detect in records of users' interactions, and even harder to replicate by abstract, generative models. Here, the authors investigate the emergence of 'trusted' users (over time) by studying the evolution of topological and centrality measures of the network of trust within the overall social network. To do so, large datasets of user activity are studied from Ciao and Epinions (two online platforms with an explicit notion of trust controlled by users), and Prosper (a micro-lending site where trust remains implicit). The implications of such findings are discussed, particularly regarding how to enable trust in online platforms and interaction, with implications for trust-based activities.