We present CAiRE-COVID, a real-time question answering (QA) and multi-document summarization system, which won one of the 10 tasks in the Kaggle COVID-19 Open Research Dataset Challenge, judged by medical experts. Our system aims to tackle the recent challenge of mining the numerous scientific articles being published on COVID-19 by answering high priority questions from the community and summarizing salient question-related information. It combines information extraction with state-of-the-art QA and query-focused multi-document summarization techniques, selecting and highlighting evidence snippets from existing literature given a query. We also propose query-focused abstractive and extractive multi-document summarization methods, to provide more relevant information related to the question. We further conduct quantitative experiments that show consistent improvements on various metrics for each module. We have launched our website CAiRE-COVID for broader use by the medical community, and have open-sourced the code for our system, to bootstrap further study by other researches.