Wide-field surveys and astronomical discovery space

I review the status of science with wide-field surveys. For many decades surveys have been the backbone of astronomy, and the main engine of discovery, as we have mapped the sky at every possible wavelength. Surveys are an efficient use of resources. They are important as a fundamental resource; to map intrinsically large structures; to gain the necessary statistics to address some problems; and to find very rare objects. I summarize major recent wide-field surveys - 2MASS, SDSS, 2dfGRS and UKIDSS - and look at examples of the exciting science they have produced, covering the structure of the Milky Way, the measurement of cosmological parameters, the creation of a new field studying substellar objects, and the ionization history of the universe. I then look briefly at upcoming projects in the optical-IR survey arena: VISTA, PanSTARRS, WISE and LSST. Finally I ask whether, now we have opened up essentially all wavelength windows, is the exploration of survey discovery space ended? I examine other possible axes of discovery space and find them mostly to be too expensive to explore or otherwise unfruitful, with two exceptions: the first is the time axis, which we have only just begun to explore properly; and the second is the possibility of neutrino astrophysics.