Immersive technologies (Virtual, Augmented, and Mixed Reality) are widely used in cultural heritage for communication, enhancing the visiting experience, and improving learning and understanding. Immersive technologies have found their way into museums and other cultural spaces in various forms and shapes. This work aims to recognize the main forms of immersive technologies and applications in museums and other cultural spaces and provide information on the employed methods, technologies, equipment, and software solutions by conducting a systematic literature review aligned with the PRISMA guidelines. The analyzed literature was collected through a focused search in scientific databases (Scopus, ACM, and IEEE). The relevance to the subject was assessed based on the main technological focus (VR/AR/MR or XR) and the employed technologies. Methods and approaches for realizing their applications were studied and discussed. Thirteen articles were found to meet the selection criteria, of which two focus on VR, six are on AR, two are on Audio-AR, and three are on MR. The results showed that Augmented Reality solutions are preferred for on-site use; Mixed Reality applications started to emerge as Mixed Reality hardware technology became available and Virtual Reality despite being criticized for isolating visitors. The findings cover the existing gap in recent literature and can reveal a set of good practices and innovative ideas for future applications.