Time series analysis stands as a focal point within the data mining community, serving as a cornerstone for extracting valuable insights crucial to a myriad of real-world applications. Recent advancements in Foundation Models (FMs) have fundamentally reshaped the paradigm of model design for time series analysis, boosting various downstream tasks in practice. These innovative approaches often leverage pre-trained or fine-tuned FMs to harness generalized knowledge tailored specifically for time series analysis. In this survey, we aim to furnish a comprehensive and up-to-date overview of FMs for time series analysis. While prior surveys have predominantly focused on either the application or the pipeline aspects of FMs in time series analysis, they have often lacked an in-depth understanding of the underlying mechanisms that elucidate why and how FMs benefit time series analysis. To address this gap, our survey adopts a model-centric classification, delineating various pivotal elements of time-series FMs, including model architectures, pre-training techniques, adaptation methods, and data modalities. Overall, this survey serves to consolidate the latest advancements in FMs pertinent to time series analysis, accentuating their theoretical underpinnings, recent strides in development, and avenues for future research exploration.