In modern society, individuals are faced with choice problems on a daily basis. In the ACQuA project, we combine methods from natural language processing and information retrieval to design a new kind ofargumentative machine for comparative question answering. Such a machine satisfies the comparative information needs of users puzzled by a choice between abundant analogous objects (e.g., digital cameras, cities as travel destinations, or programming languages). Namely, the machine acts like a human expert in a respective field, taking a question as an input and suggesting the best object choice in the given context, supporting the answer with arguments. Similar to talking to human experts, interaction with the comparative argumentative machine is performed using natural language. The main scientific challenge of the ACQuA project is to design a generic approach that yields a good coverage of objects and their aspects over various domains, as well as arguments for or against objects when compared with others but not relying on domain-specific resources. Currently, apart from singular and narrow solutions, there is no methodology for answering comparative questions in general with reasonable coverage, which is precisely what we address in ACQuA. To reach this goal, we propose a new approach involving several stages: (1) understanding comparative questions asked by users, (2) retrieving comparative argumentative structures relevant to a question from a web-scale text corpus, (3) gathering aspects of objects from a Wikipedia-based knowledge base enriched with aspects extracted from text, (4) comparison of objects on the basis of comparative argumentative structures and object aspects, (5) generation of arguments supporting the object choice, and (6) answer presentation. The key to our technology is a novel approach to argument mining that performs joint retrieval of documents relevant to the input question and extraction of complex argumentative structures from text. ACQuA will put argument mining in the context of the complex task of answering comparative questions, showing how argument mining can enable the creation of new kinds of semantic technologies. Prominent applications of the proposed comparative question answering approach are dialogue systems, decision support systems, and direct answers in web search engines.