A common feature in large-scale scientific studies is that signals are sparse and it is desirable to significantly narrow down the focus to a much smaller subset in a sequential manner. In this paper, we consider two related data screening problems: One is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals. These screening problems are closely connected to but distinct from the more conventional signal detection or multiple testing problems. We develop data-driven screening procedures which control the error rates with near optimality properties and study how to design the experiments efficiently to achieve the goals in data screening. A class of new phase diagrams is developed to characterize the fundamental limitations in simultaneous inference. An application to multistage high-throughput studies is given to illustrate the merits of the proposed screening methods.