Several novel diagnostic systems based on the detection of coherent THz radiation are presented. Among others a heterodyne setup for highest spectral resolution at 270 GHz and the fastest THz single-shot spectrometer with 500 MHz repetition rate with continuous FPGA based readout were developed and commissioned. The investigation of the photon beam properties allow for bunch-by-bunch and turn-by-turn diagnostics of the emitting electron bunches in the accelerator. It is used for time-resolved studies of the micro-bunching instability for example in the vicinity of an RF phase modulation. The accompanying simulations were performed with the Vlasov-Fokker-Planck solver Inovesa and show a good agreement of simulation and measurement which enhances the knowledge of the physics behind the micro-bunching instability.