The sixth generation (6G) networks are expected to enable immersive communications and bridge the physical and the virtual worlds. Integrating extended reality, holography, and haptics, immersive communications will revolutionize how people work, entertain, and communicate by enabling lifelike interactions. However, the unprecedented demand for data transmission rate and the stringent requirements on latency and reliability create challenges for 6G networks to support immersive communications. In this survey article, we present the prospect of immersive communications and investigate emerging solutions to the corresponding challenges for 6G. First, we introduce use cases of immersive communications, in the fields of entertainment, education, and healthcare. Second, we present the concepts of immersive communications, including extended reality, haptic communication, and holographic communication, their basic implementation procedures, and their requirements on networks in terms of transmission rate, latency, and reliability. Third, we summarize the potential solutions to addressing the challenges from the aspects of communication, computing, and networking. Finally, we discuss future research directions and conclude this study.