Conversational question answering (QA) requires answers conditioned on the previous turns of the conversation. We address the conversational QA task by decomposing it into question rewriting and question answering subtasks, and conduct a systematic evaluation of this approach on two publicly available datasets. Question rewriting is designed to reformulate ambiguous questions, dependent on the conversation context, into unambiguous questions that are fully interpretable outside of the conversation context. Thereby, standard QA components can consume such explicit questions directly. The main benefit of this approach is that the same questions can be used for querying different information sources, eg, multiple 3rd-party QA services simultaneously, as well as provide a human-readable interpretation of the question in context. To the best of our knowledge, we are the first to evaluate question rewriting on the conversational question answering task and show its improvement over the end-to-end baselines. Moreover, our conversational QA architecture based on question rewriting sets the new state of the art on the TREC CAsT 2019 dataset with a 28% improvement in MAP and 21% in NDCG@ 3. Our detailed analysis of the evaluation results provide insights into the sensitivity of QA models to question reformulation, and demonstrates the strengths and weaknesses of the retrieval and extractive QA architectures, that should be reflected in their integration.