The explosive growth of immersive and metaverse services has driven the demand for extended reality (XR) transmissions across wireless networks. XR 360 degrees video, captured by omnidirectional cameras and supported by interactive sensors, often provides users with unique immersive experiences and real-time interactions. However, the ultra-high data rate and ultra-low latency requirements for XR 360 degrees video transmissions present new signal processing challenges for XR communication systems. This paper provides a comprehensive survey of promising physical layer signal processing technologies for XR communications and systems. These include multiple antenna technologies for XR, mmWave/terahertz waves for XR communication, machine-learning-based XR transmission, and resource allocations for XR communications. Additionally, we propose a novel signal processing and transmission framework that fully exploits the space-time-frequency dimensions of virtual reality communications. Finally, we summarize the current technical challenges in signal processing for XR communications and related systems and discuss future trends in XR communications.