A concrete-filled double-skin tube (CFDST) is a new type of composite material. Experimental studies have been conducted to investigate the axial compression behavior of CFDST members for approximately 30 years. This paper provides a review of the status of axial compression bearing capacity tests conducted on circular CFDST stub columns as well as a summary of test data for 165 circular CFDST stub columns reported in 22 papers. A relatively complete high-quality test database is established. Based on this database, the main factors affecting the axial compression bearing capacity of the CFDST stub columns are analyzed. The prediction accuracy and robustness of an existing theoretical prediction model, which is a data-driven model, are evaluated, and a numerical simulation of the axial compression bearing capacity of the CFDST stub columns is conducted. In addition, the differences between the basic theory and experimental results of various models are compared, and the possible sources of prediction errors are analyzed. The current model for predicting the axial compression capacity of CFDST stub columns cannot simultaneously satisfy the requirements of high accuracy and confidence, and the stress independency assumption introduced in the test is not valid. The main error source in the theoretical prediction model is the non-simultaneous consideration of the effects of the void ratio and inner steel tube.