  This paper reviews quantum spin squeezing, which characterizes the
sensitivity of a state with respect to an SU(2) rotation, and is significant
for both entanglement detection and high-precision metrology. We first present
various definitions of spin squeezing parameters, explain their origin and
properties for typical states, and then discuss spin-squeezed states produced
with the Ising and the nonlinear twisting Hamiltonians. Afterwards, we explain
correlations and entanglement in spin-squeezed states, as well as the relations
between spin squeezing and quantum Fisher information, where the latter plays a
central role in quantum metrology. We also review the applications of spin
squeezing for detecting quantum chaos and quantum phase transitions, as well as
the influence of decoherence on spin-squeezed states. Finally, several
experiments are discussed including: producing spin squeezed states via
particle collisions in Bose-Einstein condensates, mapping photon squeezing onto
atomic ensembles, and quantum non-demolition measurements.
