Increasing the average power of broadband, few-cycle terahertz (THz) sources is currently a topic of intense investigation, fueled by recent immense progress in high average power femtosecond laser driving sources at 1030 nm. However, many crucial applications would benefit not only from an increase in average power, but also from ultra-broad bandwidth, while maintaining high dynamic range at these frequencies. This calls for the challenging combination of high repetition rates and high average power simultaneously. Here, we discuss the recent progress in the promising approach enabled by organic crystals for THz-generation. Specifically, this review article discusses advances with the most commonly used organic crystals BNA, DAST, DSTMS, OH1 and HMQ-TMS. We place special emphasis on nonlinear and thermal properties and discuss future directions for this field.