This survey provides a comprehensive and up-to-date overview of foundation models (FMs) for time series analysis. It addresses the gap in prior surveys by focusing on the underlying mechanisms of FMs in time series analysis, rather than just their applications or pipelines. The survey introduces a methodology-centric classification of TSFMs, covering key elements such as model architectures, pre-training techniques, adaptation methods, and data modalities. It highlights the theoretical foundations, recent developments, and future research directions in TSFMs. The survey discusses various types of time series, including standard time series, spatial time series, trajectories, and events. It explores the application of FMs in these domains, emphasizing their ability to capture complex temporal and spatial dependencies. The survey also presents a taxonomy of TSFMs, categorizing them based on data types, model architectures, pre-training techniques, and application domains. It further summarizes the development roadmap of current TSFMs, aiming to foster further innovations in this field. The survey covers different model architectures, including transformer-based, non-transformer-based, and diffusion-based models. It discusses the effectiveness of these models in time series analysis, highlighting their ability to capture long-range dependencies, handle sequential data, and generate realistic time series predictions. The survey also explores pre-training techniques, such as fully-supervised and self-supervised learning, and adaptation strategies, including zero-shot learning, prompt engineering, and time series tokenization. The survey also examines the use of multi-modal data in time series analysis, demonstrating how integrating different data modalities can enhance the performance of TSFMs. It discusses the potential of foundation models in various applications, including finance, healthcare, and climate forecasting. The survey concludes by emphasizing the importance of further research in this area, highlighting the potential of TSFMs in advancing time series analysis.This survey provides a comprehensive and up-to-date overview of foundation models (FMs) for time series analysis. It addresses the gap in prior surveys by focusing on the underlying mechanisms of FMs in time series analysis, rather than just their applications or pipelines. The survey introduces a methodology-centric classification of TSFMs, covering key elements such as model architectures, pre-training techniques, adaptation methods, and data modalities. It highlights the theoretical foundations, recent developments, and future research directions in TSFMs. The survey discusses various types of time series, including standard time series, spatial time series, trajectories, and events. It explores the application of FMs in these domains, emphasizing their ability to capture complex temporal and spatial dependencies. The survey also presents a taxonomy of TSFMs, categorizing them based on data types, model architectures, pre-training techniques, and application domains. It further summarizes the development roadmap of current TSFMs, aiming to foster further innovations in this field. The survey covers different model architectures, including transformer-based, non-transformer-based, and diffusion-based models. It discusses the effectiveness of these models in time series analysis, highlighting their ability to capture long-range dependencies, handle sequential data, and generate realistic time series predictions. The survey also explores pre-training techniques, such as fully-supervised and self-supervised learning, and adaptation strategies, including zero-shot learning, prompt engineering, and time series tokenization. The survey also examines the use of multi-modal data in time series analysis, demonstrating how integrating different data modalities can enhance the performance of TSFMs. It discusses the potential of foundation models in various applications, including finance, healthcare, and climate forecasting. The survey concludes by emphasizing the importance of further research in this area, highlighting the potential of TSFMs in advancing time series analysis.