Wireless communication systems exhibit structural and functional similarities to neural networks: signals propagate through cascaded elements, interact with the environment, and undergo transformations. Building upon this perspective, we introduce a unified paradigm, termed \textit{wireless physical neural networks (WPNNs)}, in which components of a wireless network, such as transceivers, relays, backscatter, and intelligent surfaces, are interpreted as computational layers within a learning architecture. By treating the wireless propagation environment and network elements as differentiable operators, new opportunities arise for joint communication-computation designs, where system optimization can be achieved through learning-based methods applied directly to the physical network. This approach may operate independently of, or in conjunction with, conventional digital neural layers, enabling hybrid communication learning pipelines. In the article, we outline representative architectures that embody this viewpoint and discuss the algorithmic and training considerations required to leverage the wireless medium as a computational resource. Through numerical examples, we highlight the potential performance gains in processing, adaptability, efficiency, and end-to-end optimization, demonstrating the promise of reconfiguring wireless systems as learning networks in next-generation communication frameworks.