Conversational question answering (ConvQA) tackles sequential informationneeds where contexts in follow-up questions are left implicit. Current ConvQAsystems operate over homogeneous sources of information: either a knowledgebase (KB), or a text corpus, or a collection of tables. This paper addressesthe novel issue of jointly tapping into all of these together, this wayboosting answer coverage and confidence. We present CONVINSE, an end-to-endpipeline for ConvQA over heterogeneous sources, operating in three stages: i)learning an explicit structured representation of an incoming question and itsconversational context, ii) harnessing this frame-like representation touniformly capture relevant evidences from KB, text, and tables, and iii)running a fusion-in-decoder model to generate the answer. We construct andrelease the first benchmark, ConvMix, for ConvQA over heterogeneous sources,comprising 3000 real-user conversations with 16000 questions, along with entityannotations, completed question utterances, and question paraphrases.Experiments demonstrate the viability and advantages of our method, compared tostate-of-the-art baselines.<br