To study the development status of wearable soft upper limb exoskeleton and its key technical challenges, the current literature in this field was analyzed and summarized. Exoskeletons can effectively provide functions such as protection and support to address limb fatigue and physical function decline resulting from high-intensity and repetitive work, as well as limb movement disorders caused by stroke or occupational diseases. Additionally, they have the capability to restore or enhance human movement ability through additional power and functionality. Wearable soft exoskeletons, as a new development direction of exoskeletons, have obvious advantages over traditional rigid exoskeletons, such as structural flexibility, human-machine interaction, and wearable comfort. Firstly, this paper provides a detailed analysis of three main driving methods of soft upper limb exoskeleton (rope drive, pneumatic, shape memory alloy). The relevant research results and corresponding structural characteristics of different driving methods are throughly examined. Then, the key technical challenges of soft upper limb exoskeleton are analyzed and expounded from four aspects: structure, material, control and auxiliary technology. Finally, considering the needs of exoskeleton applications in different fields, future trends in soft upper limb exoskeleton technology are speculated to focus on flexibility, comfort, compliance and intelligence. This study shows that the technology for wearable soft upper limb exoskeletons is still in its early stages, with many technical challenges to be solved. Futhurmore, breakthroughs in key technological challenges can be facilitated by novel soft actuators, soft sensors and other related advancements.