The nonlinear properties of zinc germanium diphosphide (ZGP) crystals enable their applications in powerful mid-IR optical parametric oscillators and second-harmonic generators. This paper summarizes the mechanisms of the laser-induced damage (LID) of high-purity ZGP crystals under periodically pulsed nanosecond irradiation by a Ho3+:YAG laser at 2.1 μm. The ZGP samples were manufactured by “LOC” Ent., Tomsk, Russia, or the Harbin Institute of Technology, China. The impact of processing techniques and the post-growing methods for polishing and anti-reflective coatings on the LID threshold are discussed. The importance of the defect structure of the crystal lattice and the parameters of transparent coatings for increasing the LID threshold are also discussed. The impact of the test laser parameters on the LID threshold and the transient area near the LID threshold obtained using digital holography are analyzed. The influence of the pre-damage processes on the optical parametric oscillations is reported. Lastly, the prospects for improving ZGP crystals to further increase the LID threshold are discussed.