Opinion formation, either within an entire society or within a smaller group, is a very complex process. In mathematical models, using dynamic systems, we simplify social interactions, view people as stylized figures, but we try to keep the most important features of communication and analyse them to reach conclusions applicable in reality. This thesis provides an overview of several simple models of opinion dynamics based on agent interactions. The main focus of the models is the problem of reaching consensus. The first chapter briefly describes some of the most well-known models of this type with discrete time. The second chapter deals with the continuous-time consensus model, in which the opinions of agents are described by a system of nonlinear differential equations. We analyzed the model with global and local interactions and described the interactions that ensure the achievement of consensus and those that lead to the division of society into so-called clusters. Computer simulations illustrated that in local dynamics, where interactions are limited to groups of agents whose opinions are not too far apart, the tendency to connect more with the different increases the likelihood of reaching consensus. The last chapter presents a modified BC (bounded confidence) model that describes a society with local interactions, limited to a radius of confidence, in the presence of a fixed signal. Simulations have shown how different combinations of confidence radius and signal strength affect the formation of agents’ opinions.