This thesis orients around argumentative characterisations of logical non-monotonic reasoning, focusing on the arbitration between conflicting claims. These characterisations are studied in terms of ar- gumentation systems. In this context, groups of inference patterns, composed of arguments for and against a claim, are produced and evaluated for the purpose of testing the acceptability of that claim. The objective of this thesis is to investigate the generalisation of argumentation systems to communicative (dialogical) interactions, in which the reasoning process is distributed among opposing agents. Under this scope a variety of issues arise such as the form of these dialectics, the development of protocols concerned with different forms of argument evaluation, strategy development for decision making, and modelling of opponent knowledge used in strategy development. This thesis makes two main contributions to the study of dialogues. The first is the provision of a dialogue framework for structured argumentation. Through this framework it is shown that the structural form of arguments needs to be taken into account when strategising, since it may have considerable impact on the outcome of a game. It is also shown that not accounting for the structural form of arguments may compromise the soundness of argument evaluation results. The second is the provision of a modelling formalism which defines how information possibly known to an opponent can be built, updated and maintained in the form of an opponent model. Part of the proposed modelling methodology relies on statistical inference and can find practical application both within the broad area of artificial intelligence and multi-agent systems as well as in other areas.