Organic pi-conjugated crystals with second-order optical nonlinearity are considerably attractive materials for diverse terahertz (THz) wave photonics. An overview of the research of organic nonlinear optical (NLO) crystals for THz wave generation, detection, and applications is provided here. First, the status of organic NLO crystals compared to other alternative THz materials is described. Second, the basic theory and requirements for organic THz generators and detectors are explained. Third, with a primary focus on the organic NLO crystals that have been developed during the last decade, various molecular engineering approaches are discussed from the perspective of THz photonics. Finally, various types of high-power broadband coherent THz sources and their applications in THz nonlinear optics are discussed.