One of the most important and fastest growing sectors of Computer Science is Artificial Intelligence. One very important and fundamental issue it deals with is Natural Language Processing, which refers to the analysis and understanding of human languages and the ability of interaction between human and ”intelligent” systems using these languages. As the volume of information is constantly increasing and people need more and more information, a very important field of research in Natural Language Processing is Question Answering. Since the beginning of the use of computers, the ability to pose questions and receiving answers from them was a fundamental objective. A very important category of question answering systems is the open-domain question answering systems, which are able to answer general knowledge questions based on an external source of knowledge, such as Wikipedia. The develoment of Transformers and BERT-based models has led to improvements in the performance of Question Answering Systems. Although these models contributed decisevely in the development of Question Answering, the fact is that most question answering systems and especially the open domain ones, work in English, while the number of systems in other languages is very limited. The present diploma thesis attempts to design and develop an open-domain question answering system in Greek. For this purpose, in the absence of the necessary datasets in Greek, machine translation is performed on some of the most suitable question answering datasets from English to Greek. Moreover, a series of models are trained for Question Answering and Information Retrieval, which is a very important part of the open-domain question answering system. Then, the overall system, which is based on the greek Wikipedia, is installed. The system is accessed by the users via a web application that has been designed and developed for this purpose. Finally, the results of the performance evaluation of the system and its components are presented.