In our lifetime there has been a marked increase in the number of ways in which people can communicate. This greater connectivity presents an added urgency for developing a solid understanding of the spread of deviant attitudes, particularly when they manifest as violent outbursts. How an otherwise moderate and rational populace can devolve to extremity through self-organisation is a question that must be answered if we hope to understand the underlying causes of atrocities that follow from extremism. That is the main question this dissertation hopes to tackle, specifically with a greater degree of realism and much less reliance on artificial manipulation than is currently present in the accepted literature of Opinion Dynamics. One such attempt at answering these questions is the Relative Agreement model, where agents are paired in order to exchange information about their own opinion. In this model, populations exhibit examples of real world convergences provided a number of initial parameters are specified. This thesis seeks to challenge and improve upon the accepted notion of the Relative Agreement model after finding fault with the published literature through the first known attempt at replication of its findings. Once a discussion of the discrepancies has been completed, a thorough analysis of the model is presented along with a number of suggested improvements to increase the capability and usefulness of the model. This examination is then followed by changing the population from a fully connected graph to a tuneable Klemm-Eguiluz social network to examine the model's properties under more realistic constraints. With this addition it was found that when agents are highly clustered, alternative population behaviours are inhibited, contrary to real world data. As a result, it is noted that the Relative Agreement model must be significantly improved upon, if it is to be applied to real world study. Once this analysis has been completed, a new model is presented, building on the Relative Agreement model and taking inspiration from Social Judgement Theory in psychology, creating the Relative Disagreement model. In this model, a disagreement dynamic is added removing the al1ificial need for pre-existing extremist agents and fixed uncertainties. It is then demonstrated that the Relative Disagreement model is able to exhibit all of the original behaviours, even with the most clustered of agent populations. Thus it can be seen that the Relative Disagreement model presented in this thesis represents a significant step forward in the understanding of extremist opinion spread and formation, the former having up until now required specific parameters to be set and the latter phenomenon being largely ignored in the field of Opinion Dynamics.