Abstract:Sky surveys represent a fundamental data basis for astronomy. We use them to map in a systematic way the universe and its constituents, and to discover new types of objects or phenomena. We review the subject, with an emphasis on the wide-field, imaging surveys, placing them in a broader scientific and historical context. Surveys are now the largest data generators in astronomy, propelled by the advances in information and computation technology, and have transformed the ways in which astronomy is done. This trend is bound to continue, especially with the new generation of synoptic sky surveys that cover wide areas of the sky repeatedly, and open a new time domain of discovery. We describe the variety and the general properties of surveys, illustrated by a number of examples, the ways in which they may be quantified and compared, and offer some figures of merit that can be used to compare their scientific discovery potential. Surveys enable a very wide range of science, and that is perhaps their key unifying characteristic. As new domains of the observable parameter space open up thanks to the advances in technology, surveys are often the initial step in their exploration. Some science can be done with the survey data alone (or a combination of data from different surveys), and some requires a targeted follow-up of potentially interesting sources selected from surveys. Surveys can be used to generate large, statistical samples of objects that can be studied as populations, or as tracers of larger structures to which they belong. They can be also used to discover or generate samples of rare or unusual objects, and may lead to discoveries of some previously unknown types. We discuss a general framework of parameter spaces that can be used for an assessment and comparison of different surveys, and the strategies for their scientific exploration. As we are moving into the Petascale regime and beyond, an effective processing and scientific exploitation of such large data sets and data streams poses many challenges, some of which are specific to any given survey, and some of which may be addressed in the framework of Virtual Observatory and Astroinformatics. The exponential growth of data volumes and complexity makes a broader application of data mining and knowledge discovery technologies critical in order to take a full advantage of this wealth of information. Finally, we discuss some outstanding challenges and prospects for the future.* We dedicate this chapter to the memory of three pioneers of sky surveys, Fritz Zwicky (1898-1974), Bogdan Paczynski (1940), and John Huchra (1948