Since trust is one of the most important factors in forming social interactions, it is necessary in these networks to evaluate trust from one user to another indirectly connected user, using propagating trust along reliable trust paths between the two users. The quality of trust inference based on trust propagation is affected by the length of trust paths and also different aggregation and propagation strategies for propagating and combining trust values. In this chapter, we first review existing methods in the literature for the trust inference and then introduce two learning automata based trust propagation algorithms DLATrust and DyTrust in details. The algorithm DLATrust utilizes distributed learning automata to discover reliable trust paths and predict the trust value between two indirectly connected users. The algorithm DyTrust is a dynamic trust propagation algorithm based on distributed learning automata for inferring trust in stochastic trust networks. Since trust changes over time as a result of repeated direct interactions between users, trust networks can be modelled as stochastic graphs with continuous time-varying edge weights. Even though the dynamic nature of trust has been universally accepted in literature, existing trust propagation algorithms do not take the dynamicity of trust into consideration. These algorithms take an instant snapshot of trust network and then deterministically infer trust in the network snapshot. Due to being time consuming of trust propagation algorithms, it is highly probable that trust weights change during the algorithms’ running time and therefore the estimated trust values will not have enough accuracy. DyTrust is the first to address the dynamicity property of trust in the domain of trust inference. Considering the changes of trust weights in time, this algorithm finds the most reliable trust path to each neighboring user of target and estimates the trust value of the target based on its neighbors’ reliability.