We review recent research using organic materials for generation and detection of broadband terahertz radiation (0.3 THz−30 THz). The main focus is on amorphous electrooptic (EO) polymers, with semiconducting polymers, molecular salt EO crystals, and molecular solutions briefly discussed. The advantages of amorphous EO polymers over other materials for broadband THz generation (via optical rectification) and detection (via EO sampling) include a lack of phonon absorption (good transparency) in the THz regime, high EO coefficient and good phase-matching properties, and, of course, easy fabrication (low cost). Our ∼12-THz, spectral gap-free THz system based on a polymer emitter-sensor pair is an excellent demonstration of the advantages using of EO polymers. We also present a model that can predict the performance of a polymer-based THz system. Both the dielectric properties of an EO polymer and laser pulse related parameters are included in the model, making the simulations close to real conditions. From our modeling work, the roles the dielectric properties play in the THz generation and detection are clearly seen, providing us with a good guide to select and design suitable EO polymers in the future.