The distribution pattern and root causes of fractures resulting from hydraulic fracturing in coalbed methane (CBM) reservoirs significantly affect the effectiveness of reservoir stimulation. A thorough understanding of the characteristics and propagation mechanism of hydraulic fractures is crucial for the efficient development of CBM, and also serves as a fundamental basis for optimizing the parameters of the hydraulic fracturing process. Based on the current situation of CBM reservoirs hydraulic fracturing development both domestically and internationally, this study analyzes the characteristics and differences of various methods for physical experiments, theoretical models, and numerical simulations. Additionally, it systematically reviews the influence mechanism of internal geological factors and external engineering factors on the fracture propagation behavior of CBM reservoir. Also it summarizes the current problems and trends in the hydraulic fracture research. The results show that configuring acoustic emission monitoring and optical imaging components in the true triaxial physical experiment could greatly promote the study on the mechanical behavior and extension path of hydraulic fractures. The theoretical models can effectively quantify the behavior of hydraulic fractures, but the preset fracture shape and extension path of different fractures may cause some deviations from actual production. Numerical simulation can explore the dynamic formation process of the hydraulic fracture network controlled by multiple geological factors under the in-situ condition of reservoir and the interaction among multiple fractures. Furthermore, the hydraulic fracturing of the CBM reservoirs is a comprehensive process constrained by multi-factors such as natural weak plane, in-situ stress, coal macro-lithotype, coal structure, and proppant. Future researches should focus on ① Realizing a real-time monitoring of fracture behavior under in-situ temperature and pressure conditions in the large-scale hydraulic fracturing physical experiments and forming a sample preparation standard; ② Thoroughly studying the superposition effect of natural fracture geometry and hydraulic fracturing engineering parameters (e.g. water injection rate and fracturing fluid viscosity) on the interaction mode of hydraulic fractures in the basic theoretical models; ③ Applying the microseismic monitoring data of field fracturing to optimize the geometric shape and expansion path setting of natural fractures and hydraulic fractures in the numerical simulation; and ④ Quantifying the coupling effect of multi-fields and geological factors on hydraulic fracture networks.