We introduce LEAF-QA, a comprehensive dataset of 250,000 densely annotated figures/charts, constructed from real-world open data sources, along with ~2 million question-answer (QA) pairs querying the structure and semantics of these charts. LEAF-QA highlights the problem of multimodal QA, which is notably different from conventional visual QA (VQA), and has recently gained interest in the community. Furthermore, LEAF-QA is significantly more complex than previous attempts at chart QA, viz. FigureQA and DVQA, which present only limited variations in chart data. LEAF-QA being constructed from real-world sources, requires a novel architecture to enable question answering. To this end, LEAF-Net, a deep architecture involving chart element localization, question and answer encoding in terms of chart elements, and an attention network is proposed. Different experiments are conducted to demonstrate the challenges of QA on LEAF-QA. The proposed architecture, LEAF-Net also considerably advances the current state-of-the-art on FigureQA and DVQA.