Microfluidic systems are an attractive solution for the miniaturization of biological and chemical assays. The typical sample volume can be reduced up to 1 million-fold, and a superb level of spatiotemporal control is possible, facilitating highly parallelized assays with drastically increased throughput and reduced cost. In this review, we focus on systems in which multiple reactions are spatially separated by immobilization of reagents on two-dimensional arrays, or by compartmentalization in microfabricated reaction chambers or droplets. These systems have manifold applications, and some, such as next-generation sequencing are already starting to transform biology. This is likely the first step in a biotechnological transformation comparable to that already brought about by the microprocessor in electronics. We discuss both current applications and likely future impacts in areas such as the study of single cells/single organisms and high-throughput screening.