To meet the stringent requirements for high-performance structural materials in the aerospace sector, high-entropy alloys (HEAs) have emerged as critical candidate materials owing to their unique design philosophy and distinctive performance characteristics. This work focuses on three typical HEA systems, namely refractory HEAs, lightweight HEAs, and eutectic HEAs. It systematically analyzes the representative compositions, microstructural features, and performance advantages of the three alloy systems, as well as the major technical bottlenecks and corresponding breakthrough approaches in core aerospace application scenarios such as ultra-high temperature service and lightweight design. By analyzing the research and development progress in major countries and regions worldwide, this work identifies the developmental trend of HEAs shifting from theoretical exploration to demand-driven research. It also sorts out the common scientific and technical challenges concerning composition design, fabrication, and performance evaluation that urgently need to be addressed for the engineering application of HEAs in aerospace, which are summarized as follows: (1) design and screening of HEAs component systems that break through the performance limits of conventional materials; (2) integrated computation and high-throughput rapid optimization technologies for the vast compositional space of HEAs; (3) high-quality and high-efficiency fabrication and forming technologies for complex HEAs components; (4) determination of cost-effective composition ranges that realize the coordinated optimization of mechanical performance and production cost for HEAs; (5) comprehensive performance assessment and database construction targeting extreme service environments. Furthermore, this work puts forward a forward-looking prospect on the future technological development directions of aerospace HEAs, aiming to provide theoretical support and technical references for accelerating the transformation of HEAs from fundamental research to vital engineering applications.