Foundation Models (FMs) such as GPT-4 encoded with vast knowledge and powerful emergent abilities have achieved remarkable success in various natural language processing and computer vision tasks. Grounding FMs by adapting them to domain-specific tasks or augmenting them with domain-specific knowledge enables us to exploit the full potential of FMs. However, grounding FMs faces several challenges, stemming primarily from constrained computing resources, data privacy, model heterogeneity, and model ownership. Federated Transfer Learning (FTL), the combination of federated learning and transfer learning, provides promising solutions to address these challenges. In recent years, the need for grounding FMs leveraging FTL, coined FTL-FM, has arisen strongly in both academia and industry. Motivated by the strong growth in FTL-FM research and the potential impact of FTL-FM on industrial applications, we propose an FTL-FM framework that formulates problems of grounding FMs in the federated learning setting, construct a detailed taxonomy based on the FTL-FM framework to categorize state-of-the-art FTL-FM works, and comprehensively overview FTL-FM works based on the proposed taxonomy. We also establish correspondences between FTL-FM and conventional phases of adapting FM so that FM practitioners can align their research works with FTL-FM. In addition, we overview advanced efficiency-improving and privacy-preserving techniques because efficiency and privacy are critical concerns in FTL-FM. Last, we discuss opportunities and future research directions of FTL-FM.