The task of Question Answering (QA) is arguably one of the oldest tasks in Natural Language Processing, attracting high levels of interest from both industry and academia. However, most research has focused on factoid questions, e.g. Who is the president of Ireland? In contrast, research on answering non-factoid questions, such as manner, reason, difference and opinion questions, has been rather piecemeal. This was largely due to the absence of available labelled data for the task. This is changing, however, with the growing popularity of Community Question Answering (CQA) websites, such as Quora, Yahoo! Answers and the Stack Exchange family of forums. These websites provide natural labelled data allowing us to apply machine learning techniques. Most previous state-of-the-art approaches to the tasks of CQA-based question answering involved handcrafted features in combination with linear models. In this thesis we hypothesise that the use of handcrafted features can be avoided and the tasks can be approached with representation learning techniques, specifically deep learning. In the first part of this thesis we give an overview of deep learning in natural language processing and empirically evaluate our hypothesis on the task of detecting semantically equivalent questions, i.e. predicting if two questions can be answered by the same answer. In the second part of the thesis we address the task of answer ranking, i.e. determining how suitable an answer is for a given question. In order to determine the suitability of representation learning for the task of answer ranking, we provide a rigorous experimental evaluation of various neural architectures, based on feedforward, recurrent and convolutional neural networks, as well as their combinations. This thesis shows that deep learning is a very suitable approach to CQA-based QA, achieving state-of-the-art results on the two tasks we addressed.