While initial applications of artificial intelligence (AI) in wireless communications over the past decade have demonstrated considerable potential using specialized models for targeted communication tasks, the revolutionary demands of sixth-generation (6G) networks for holographic communications, ubiquitous sensing, and native intelligence are propelling a necessary evolution towards AI-native wireless networks. The arrival of large AI models paves the way for the next phase of Wireless AI, driven by wireless foundation models (WFMs). In particular, pre-training on universal electromagnetic (EM) principles equips WFMs with the essential adaptability for a multitude of demanding 6G applications. However, existing large AI models face critical limitations, including pre-training strategies disconnected from EM-compliant constraints leading to physically inconsistent predictions, a lack of embedded understanding of wave propagation physics, and the inaccessibility of massive labeled datasets for comprehensive EM-aware training. To address these challenges, this article presents an electromagnetic information theory-guided self-supervised pre-training (EIT-SPT) framework designed to systematically inject EM physics into WFMs. The EIT-SPT framework aims to infuse WFMs with intrinsic EM knowledge, thereby enhancing their physical consistency, generalization capabilities across varied EM landscapes, and overall data efficiency. Building upon the proposed EIT-SPT framework, this article first elaborates on diverse potential applications in 6G scenarios of WFMs, then validates the efficacy of the proposed framework through illustrative case studies, and finally summarizes critical open research challenges and future directions for WFMs.