The interactive holographic display technology, due to its unique true three-dimensional (3D) display ability, can bring users a natural and real human-computer interactive mode. As an important part of the interactive holographic display system, the gesture recognition module has an important impact on the success, nature and comfort of the interaction process. There are mainly three gesture recognition ways in the interactive holographic display system, recognition based on wearable devices, recognition based on visual inspection, and 3D touch detection based on holographic 3D display. The research progress of the interactive holographic display system is firstly reviewed, then the development, merits and faults of these three interactive modes are discussed, and the current problems and development prospects of the interactive holographic display system are finally analyzed. This study can provid a reference for the further research on the interactive holographic display.