The rise of large language models (LLMs), such as ChatGPT, Gemini, and Grok, has reshaped the AI landscape. As prominent instances of foundational models (FMs), they exhibit remarkable capabilities in generating human-like content, pushing the boundaries towards artificial general intelligence (AGI). However, their large-scale nature, privacy sensitivity, and substantial computational demands pose significant challenges for personalized customization for end users. To bridge this gap, we present the vision of artificial personalized intelligence (API), which focuses on adapting FMs to individual users while ensuring privacy. As a central enabler of API, we propose personalized federated intelligence (PFI), a new paradigm that not only integrates the privacy benefits of federated learning (FL) with the generalization capabilities of FMs but also places personalization at its core. To this end, we first survey recent advances in FL and FMs that lay the foundation for PFI. We then explore core stages of the PFI pipeline: efficient personalization at the edge, trustworthy adaptation, and adaptive refinement via retrieval-augmented generation. Finally, we highlight future directions for enabling PFI. Overall, this survey aims to lay a foundation for the development of API as a complementary direction to AGI, with PFI as a key enabling paradigm.