This thesis focuses on using (computational) argumentation theory to model common-sense reasoning with preferences. Common-sense reasoning entails dealing with incomplete, uncertain and conflicting information. Argumentation as a branch of Artificial Intelligence (AI) provides means to reason with such information in a formal way. An important aspect of commonsense reasoning is reasoning with preference information. As such, dealing with preferences is an important phenomenon in argumentation. Through our research, we aim to contribute to the understanding of preference information treatment in argumentation and common-sense reasoning, as well as AI at large. Our objective is to equip a well established structured argumentation formalism - Assumption-Based Argumentation (ABA) - with a new preference handling mechanism. To this end, we propose an extension of ABA, called ABA+, where preferences are accounted for by reversing attacks. This yields a novel way of dealing with preference information in structured argumentation. We also advance a new property concerning contraposition of rules, called Weak Contraposition, applicable to ABA+, and, potentially, to generic approaches to rule-based reasoning with preferences. We argue that ABA+ (with and without Weak Contraposition) exhibits various desirable formal properties concerning argumentation and/or preference handling. We analyse ABA+ in the context of other formalisms of argumentation with preferences and contend advantages of ABA+.