During the past decade, various new types of organic nonlinear optical crystals have been developed to overcome the benchmark stilbazolium DAST (4-(4-(N, N-dimethylamino) styryl)-1-methylpyridinium 4-methylbenzenesulfonate) crystal. Here, we review the acentric core structures used in recently developed organic nonlinear optical crystals exhibiting high macroscopic second-order optical nonlinearity, along with their supramolecular interactions and THz applications. The nonlinear optical acentric core structures such as neutral CLP (configurationally locked polyene based on phenyltriene), ionic pyridinium-based N-alkyl DAS (4-(4-(N, N-dimethylamino) styryl)-1-alkylpyridinium benzenesulfonate) and N-phenyl DAP ((4-(N, N-dimethylamino) styryl)-1-phenylpyridinium hexafluorophosphate), ionic quinolinium-based HMQ (2-(4-hydroxy-3-methoxystyryl)-1-methylquinolinium benzenesulfonate) and OHQ (2-(4hydroxystyryl)-1-methylquinolinium benzenesulfonate) and benzoindolium-based DBI (2-(4(dimethylamino) styryl)-1,3,3-trimethyl-3H-benzo[g] indolium iodide) exhibit comparable or enhanced physical properties compared to DAST crystals. Organic crystals introducing an identical acentric core structure often exhibit similar molecular alignment features with analogous supramolecular interactions. We also discuss the nonlinear optical properties and potential applications of these materials, in particular their very promising THz photonic applications.