  Low-cost mass-produced sensors and optics have recently made it feasible to
build telescope arrays which observe the entire accessible sky simultaneously.
In this article we discuss the scientific motivation for these telescopes,
including exoplanets, stellar variability and extragalactic transients. To
provide a concrete example we detail the goals and expectations for the
Evryscope, an under-construction 780 MPix telescope which covers 8,660 square
degrees in each two-minute exposure; each night, 18,400 square degrees will be
continuously observed for an average of approximately 6 hours. Despite its
small 61mm aperture, the system's large field of view provides an etendue which
is ~10% of LSST. The Evryscope, which places 27 separate individual telescopes
into a common mount which tracks the entire accessible sky with only one moving
part, will return 1%-precision, many-year-length, high-cadence light curves for
every accessible star brighter than mV=16.5, with brighter stars having
few-millimagnitude photometric precision in long-term light curves. It will be
capable of searching for transiting giant planets around the brightest and most
nearby stars, where the planets are much easier to characterize; it will also
search for small planets nearby M-dwarfs, for planetary occultations of white
dwarfs, and will perform comprehensive nearby microlensing and eclipse-timing
searches for exoplanets inaccessible to other planet-finding methods. The
Evryscope will also monitor outbursting young stars, white dwarf activity, and
stellar activity of all types, along with finding a large sample of
very-long-period M-dwarf eclipsing binaries. When relatively rare transients
events occur, such as gamma-ray bursts (GRBs), nearby supernovae, or even
gravitational wave detections, the array will return minute-by-minute light
curves without needing pointing towards the event as it occurs. (abridged)
