Our news are saturated with claims of "facts" made from data. Database research has in the past focused on how to answer queries, but has not devoted much attention to discerning more subtle qualities of the resulting claims, e.g., is a claim "cherry-picking"? In this talk, I will describe a framework that we developed recently for checking facts based on queries over structured data. This framework lets us formulate practical fact-checking tasks---such as reverse-engineering (often intentionally) vague claims, and countering questionable claims---as computational problems. I will also describe some algorithmic and system-building challenges that arise in this framework.