The increasing necessity of load-carrying activities has led to greater human musculoskeletal damage and an increased metabolic cost. With the rise of exoskeleton technology, researchers have begun exploring different approaches to developing wearable robots to augment human load-carrying ability. However, there is a lack of systematic discussion on biomechanics, mechanical designs, and augmentation performance. To achieve this, extensive studies have been reviewed and 108 references are selected mainly from 2013 to 2022 to address the most recent development. Other earlier 20 studies are selected to present the origin of different design principles. In terms of the way to achieve load-carrying augmentation, the exoskeletons reviewed in this paper are sorted by four categories based on the design principles, namely load-suspended backpacks, lower-limb exoskeletons providing joint torques, exoskeletons transferring load to the ground and exoskeletons transferring load between body segments. Specifically, the driving modes of active and passive, the structure of rigid and flexible, the conflict between assistive performance and the mass penalty of the exoskeleton, and the autonomy are discussed in detail in each section to illustrate the advances, challenges, and future trends of exoskeletons designed to carry loads.