Hydrogen is an ideal energy carrier in future applications due to clean byproducts and high efficiency. However, many challenges remain in the application of hydrogen, including hydrogen production, delivery, storage and conversion. In terms of hydrogen storage, two compression modes (mechanical and non-mechanical compressors) are generally used to increase volume density in which mechanical compressors with several classifications including reciprocating piston compressors, hydrogen diaphragm compressors and ionic liquid compressors produce significant noise and vibration and are expensive and inefficient. Alternatively, non-mechanical compressors are faced with issues involving large-volume requirements, slow reaction kinetics and the need for special thermal control systems, all of which limit large-scale development. As a result, modular, safe, inexpensive and efficient methods for hydrogen storage are urgently needed. And because electrochemical hydrogen compressors (EHCs) are modular, highly efficient and possess hydrogen purification functions with no moving parts, they are becoming increasingly prominent. Based on all of this and for the first time, this review will provide an overview of various hydrogen compression technologies and discuss corresponding structures, principles, advantages and limitations. This review will also comprehensively present the recent progress and existing issues of EHCs and future hydrogen compression techniques as well as corresponding containment membranes, catalysts, gas diffusion layers and flow fields. Furthermore, engineering perspectives are discussed to further enhance the performance of EHCs in terms of the thermal management, water management and the testing protocol of EHC stacks. Overall, the deeper understanding of potential relationships between performance and component design in EHCs as presented in this review can guide the future development of anticipated EHCs.