How should statistical procedures be designed so as to be scalable computationally to the massive datasets that are increasingly the norm? When coupled with the requirement that an answer to an inferential question be delivered within a certain time budget, this question has significant repercussions for the field of statistics. With the goal of identifying "time-data tradeoffs," we investigate some of the statistical consequences of computational perspectives on scability, in particular divide-and-conquer methodology and hierarchies of convex relaxations.