The increasing generation and collection of personal data has created a complex ecosystem, often collaborative but sometimes combative, around companies and individuals engaging in the use of these data. We propose that the interactions between these agents warrants a new topic of study: Human-Data Interaction (HDI). In this paper we discuss how HDI sits at the intersection of various disciplines, including computer science, statistics, sociology, psychology and behavioural economics. We expose the challenges that HDI raises, organised into three core themes of legibility, agency and negotiability, and we present the HDI agenda to open up a dialogue amongst interested parties in the personal and big data ecosystems.