The integration of Foundation Models (FMs) with Federated Learning (FL) presents a transformative paradigm in Artificial Intelligence (AI), offering enhanced capabilities while addressing concerns of privacy, data decentralization, and computational efficiency. This paper provides a comprehensive survey of the emerging field of Federated Foundation Models (FedFM), elucidating their synergistic relationship and exploring novel methodologies, challenges, and future directions that the FL research field needs to focus on in order to thrive in the age of foundation models. A systematic multi-tiered taxonomy is proposed, categorizing existing FedFM approaches for model training, aggregation, trustworthiness, and incentivization. Key challenges, including how to enable FL to deal with high complexity of computational demands, privacy considerations, contribution evaluation, and communication efficiency, are thoroughly discussed. Moreover, the paper explores the intricate challenges of communication, scalability and security inherent in training/fine-tuning FMs via FL, highlighting the potential of quantum computing to revolutionize the training, inference, optimization and data encryption processes. This survey underscores the importance of further research to propel innovation in FedFM, emphasizing the need for developing trustworthy solutions. It serves as a foundational guide for researchers and practitioners interested in contributing to this interdisciplinary and rapidly advancing field.