Extended reality (XR) is a key innovation of 5G-advanced and beyond networks. The diverse XR use-cases, including virtual reality, augmented reality, and mixed reality, transform the way humans interact with surrounding environments. Thus, XR technology enables true immersive experiences of novel services spanning, e.g., e-commerce, healthcare, and education, respectively. However, the efficient support of XR services over existing and future cellular systems is highly challenging and requires multiple radio design improvements, due to the unique XR traffic and performance characteristics. Thus, this article surveys the state-of-art 3GPP standardization activities (release-18) for integrating the XR service class into the 5G-advanced specifications, highlighting the major XR performance challenges. Furthermore, the paper introduces valuable insights and research directions for supporting true XR services over the next-generation 6G networks, where multiple novel radio design mindsets and protocol enhancements are proposed and evaluated using extensive system level simulations, including solutions for application-native dynamic performance reporting, traffic-dependent control channel design, collaborative device aggregation for XR capacity boosting and offload, respectively.