Current tools for exploratory data analysis (EDA) require users to manually select data attributes, statistical computations and visual encodings. This can be daunting for large-scale, complex data. We introduce Foresight, a system that helps the user rapidly discover visual insights from large high-dimensional datasets. Formally, an "insight" is a strong manifestation of a statistical property of the data, e.g., high correlation between two attributes, high skewness or concentration about the mean of a single attribute, a strong clustering of values, and so on. For each insight type, Foresight initially presents visualizations of the top k instances in the data, based on an appropriate ranking metric. The user can then look at "nearby" insights by issuing "insight queries" containing constraints on insight strengths and data attributes. Thus the user can directly explore the space of insights, rather than the space of data dimensions and visual encodings as in other visual recommender systems. Foresight also provides "global" views of insight space to help orient the user and ensure a thorough exploration process. Furthermore, Foresight facilitates interactive exploration of large datasets through fast, approximate sketching.