Argumentation, in one form or another, is and has always been present in our lives. Although it has its origins in the field of philosophy, it has expanded with time and, with the recent development in computer science, also established itself as an area in artificial intelligence. Within it, we distinguish abstract argumentation, in which we consider arguments as atomic entities and focus entirely on the relations between them. One of the most prominent argumentation frameworks is the one due to Dung. It allows us to express binary attack between arguments. Throughout the years, a number of generalizations was proposed, including but not limited to the frameworks that extend the basic system with more advanced relations between arguments, such as the framework for arguing with sets of attacking arguments (SETAF), argumentation framework with recursive attacks (AFRA), extended argumentation framework (EAF) and its collective version (EAFC), bipolar argumentation framework (BAF), argumentation framework with necessities (AFN), and evidential argumentation system (EAS). Amongst the most general frameworks in this group we can find the abstract dialectical frameworks (ADFs for short), which unlike other formalisms, use so--called acceptance conditions to express under what circumstances a given argument can be accepted or rejected. This work is devoted to the study of ADFs as well as of the aforementioned structures. This thesis is organized as follows. We first focus on the development of semantics for ADFs. As an alternative to the labeling-based approaches, we propose a number of extension--based methods, which focus primarily on the acceptance of arguments and pay particular attention to the issue of support cycles in argumentation. We then analyze all of these semantics and show that, in principle, one cannot replace another. We also provide preliminary complexity results for the usual verification, skeptical and credulous reasoning problems for our approaches. With these semantics we can now show how ADFs can be placed in the field of argumentation. In doing so, we provide an extensive study on the topic of framework intertranslatability and create an in-depth compendium consisting of almost ninety translations between all of the listed formalisms. Furthermore, we introduce a classification system which can be used to organize our methods as well as the ones that might be introduced in the future. Our results show that ADFs are indeed powerful frameworks that can handle a wide range of other formalisms, even those that could be compared together only under various restrictions. Moreover, unlike many other frameworks, ADFs have been implemented and there are various results concerning their complexity, realizability and instantiations. All of this makes them good candidates both for further research and for developing practical solutions.