X-ray-induced acoustic computed tomography (XACT) offers a promising approach to biomedical imaging, leveraging X-ray absorption contrast. It overcomes the shortages of traditional X-ray, allowing for more advanced medical imaging. The review focuses on the significance and draws onto the potential applications of XACT to demonstrate it as an innovative imaging technique. This review navigates the expanding landscape of XACT imaging within the biomedical sphere. Integral topics addressed encompass the refinement of imaging systems and the advancement in image reconstruction algorithms. The review particularly emphasizes XACT's significant biomedical applications. Key uses, such as breast imaging, bone density maps for osteoporosis, and X-ray molecular imaging, are highlighted to demonstrate the capability of XACT. A unique niche for XACT imaging is its application in in vivo dosimetry during radiotherapy, which has been validated on patients. Because of its unique property, XACT has great potential in biomedicine and non-destructive testing. We conclude by casting light on potential future avenues in this promising domain.