In this review we discuss the application of laser-induced breakdown spectroscopy (LIBS) to the problem of detection of residues of explosives. Research in this area presented in open literature is reviewed. Both laboratory and field-tested standoff LIBS instruments have been used to detect explosive materials. Recent advances in instrumentation and data analysis techniques are discussed, including the use of double-pulse LIBS to reduce air entrainment in the analytical plasma and the application of advanced chemometric techniques such as partial least-squares discriminant analysis to discriminate between residues of explosives and non-explosives on various surfaces. A number of challenges associated with detection of explosives residues using LIBS have been identified, along with their possible solutions. Several groups have investigated methods for improving the sensitivity and selectivity of LIBS for detection of explosives, including the use of femtosecond-pulse lasers, supplemental enhancement of the laser-induced plasma emission, and complementary orthogonal techniques. Despite the associated challenges, researchers have demonstrated the tremendous potential of LIBS for real-time detection of explosives residues at standoff distances.