This article presents a wireless neural processing architecture (WiNPA), providing a novel perspective for accelerating edge inference of deep neural network (DNN) workloads via joint optimization of wireless and computing resources. WiNPA enables fine-grained integration of wireless communication and edge computing, bridging the research gap between wireless and edge intelligence and significantly improving DNN inference performance. To fully realize its potential, we explore a set of fundamental research issues, including mathematical modeling, optimization, and unified hardware--software platforms. Additionally, key research directions are discussed to guide future development and practical implementation. A case study demonstrates WiNPA's workflow and effectiveness in accelerating DNN inference through simulations.