Event Causality Identification (ECI) has become a crucial task in Natural Language Processing (NLP), aimed at automatically extracting causalities from textual data. In this survey, we systematically address the foundational principles, technical frameworks, and challenges of ECI, offering a comprehensive taxonomy to categorize and clarify current research methodologies, as well as a quantitative assessment of existing models. We first establish a conceptual framework for ECI, outlining key definitions, problem formulations, and evaluation standards. Our taxonomy classifies ECI methods according to the two primary tasks of sentence-level (SECI) and document-level (DECI) event causality identification. For SECI, we examine feature pattern-based matching, deep semantic encoding, causal knowledge pre-training and prompt-based fine-tuning, and external knowledge enhancement methods. For DECI, we highlight approaches focused on event graph reasoning and prompt-based techniques to address the complexity of cross-sentence causal inference. Additionally, we analyze the strengths, limitations, and open challenges of each approach. We further conduct an extensive quantitative evaluation of various ECI methods on two benchmark datasets. Finally, we explore future research directions, highlighting promising pathways to overcome current limitations and broaden ECI applications.