With the development of next-generation wireless networks, the Internet of Things (IoT) is evolving towards the intelligent IoT (iIoT), where intelligent applications usually have stringent delay and jitter requirements. In order to provide low-latency services to heterogeneous users in the emerging iIoT, multi-tier computing was proposed by effectively combining edge computing and fog computing. More specifically, multi-tier computing systems compensate for cloud computing through task offloading and dispersing computing tasks to multi-tier nodes along the continuum from the cloud to things. In this paper, we investigate key techniques and directions for wireless communications and resource allocation approaches to enable task offloading in multi-tier computing systems. A multi-tier computing model, with its main functionality and optimization methods, is presented in details. We hope that this paper will serve as a valuable reference and guide to the theoretical, algorithmic, and systematic opportunities of multi-tier computing towards next-generation wireless networks.