Heterogeneous multi-radio networks are emerging network architectures, which comprise hierarchical deployments of increasingly smaller cells. In these deployments, each user device may employ multiple radio access technologies to communicate with network infrastructure. With the growing numbers of such multi-radio consumer devices, mobile network operators seek to leverage spectrum across diverse radio technologies thus boosting capacity and enhancing quality of service. In this article, we review major challenges in delivering uniform connectivity and service experience to converged multi-radio heterogeneous deployments. We envision that multiple radios and associated device/infrastructure intelligence for their efficient use will become a fundamental characteristic of future 5G technologies, where the distributed unlicensed-band network (e.g., WiFi) may take advantage of the centralized control function residing in the cellular network (e.g., 3GPP LTE). Illustrating several available architectural choices for integrating WiFi and LTE networks, we specifically focus on interworking within the radio access network and detail feasible options for intelligent access network selection. Both networkand user-centric approaches are considered, wherein the control rests with the network or the user. In particular, our system-level simulation results indicate that load-aware user-centric schemes, which augment SNR measurements with additional information about network loading, could improve the performance of conventional WiFi-preferred solutions based on minimum SNR threshold. Comparison with more advanced network-controlled schemes has also been completed to confirm attractive practical benefits of distributed user-centric algorithms. Building on extensive system-wide simulation data, we also propose novel analytical space-time methodology for assisted network selection capturing user traffic dynamics together with spatial randomness of multi-radio heterogeneous networks.