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.
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