Social media platforms provide a goldmine for mining public opinion on issues of wide societal interest. Opinion mining is a problem that can be operationalised by capturing and aggregating the stance of individual social media posts as supporting, opposing or being neutral towards the issue at hand. While most prior work in stance detection has investigated datasets with limited time coverage, interest in investigating longitudinal datasets has recently increased. Evolving dynamics in linguistic and behavioural patterns observed in new data require in turn adapting stance detection systems to deal with the changes. In this survey paper, we investigate the intersection between computational linguistics and the temporal evolution of human communication in digital media. We perform a critical review in emerging research considering dynamics, exploring different semantic and pragmatic factors that impact linguistic data in general, and stance particularly. We further discuss current directions in capturing stance dynamics in social media. We organise the challenges of dealing with stance dynamics, identify open challenges and discuss future directions in three key dimensions: utterance, context and influence.