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Precursor emissions are found in some short gamma-ray bursts (SGRBs). In this paper, we review the theories and observations of the SGRB precursor and discuss its prospect as an electromagnetic counterpart of the gravitational wave event produced by neutron star (NS) mergers. The observed luminosity, spectrum, and duration of precursors are explained by the magnetospheric interaction model during the inspiral or the cocoon/jet shock breakout model during the jet propagation. In general, these two models predict that the precursor will be weaker than the main GRB, but will be of a larger opening angle, which makes it an advantageous gamma-ray counterpart for NS mergers in the local Universe, especially for NS - black hole mergers with very low mass ratios, in which the main GRBs are not expected. The joint observation of the precursor, SGRB, and gravitational wave will help to reveal the jet launch mechanism and post-merger remnant. [ABSTRACT FROM AUTHOR]