Network slicing is considered a key feature of 5G and beyond cellular systems. It opens the door for new business models of mobile operators, enables new services, reduces costs with advanced infrastructure-sharing techniques, and improves heterogeneous traffic service. With slicing, the operators can tailor the network resources to the requirements of specific verticals, applications, and corresponding traffic types. To satisfy the heterogeneous quality of service (QoS) requirements of various slices, efficient virtualization and resource allocation algorithms are required. Such algorithms are especially crucial for the radio access network (RAN) because of the spectrum scarcity. This article develops DeSlice, a novel architecture for RAN slicing. DeSlice enables efficient real-time slicing algorithms that satisfy heterogeneous QoS requirements of the slices and improve the quality of experience for their end users. The article illustrates the advantages of DeSlice by considering the problem of the joint service of cloud VR, video, and web traffic. It develops the algorithms using DeSlice architecture and application-to-network communication. With simulations, it shows that, together, the architecture and the algorithms allow greatly improving the QoE for these traffics significantly.