Social media tends to be rife with rumours when new reports are released piecemeal during breaking news events. One can mine multiple reactions expressed by social media users in those situations, exploring users’ stance towards rumours, ultimately enabling the flagging of highly disputed rumours as being potentially false. Moreover, rumours in social media exhibit complex temporal patterns. Some rumours are discussed with an increasing number of tweets per unit of time whereas other rumours fail to gain ground. This thesis develops probabilistic models of rumours in social media driven by two applications: rumour stance classification and modeling temporal dynamics of rumours. Rumour stance classification is the task of classifying the stance expressed in an individual tweet towards a rumour. Modeling temporal dynamics of rumours is an application where rumour prevalence is modeled over time. Both applications provide insights into how a rumour attracts attention from the social media community. These can assist journalists with their work on rumour tracking and debunking, and can be used in downstream applications such as systems for rumour veracity classification. In this thesis, we develop models based on probabilistic approaches. We motivate Gaussian processes and point processes as appropriate tools and show how features not considered in previous work can be included. We show that for both applications, transfer learning approaches are successful, supporting the hypothesis that there is a common underlying signal across different rumours. We furthermore introduce novel machine learning techniques which have the potential to be used in other applications: convolution kernels for streams of text over continuous time and a sequence classification algorithm based on point processes.