<p>Aspect sentiment triplet extraction (ASTE) in natural language processing focuses on the automatic identification and extraction of aspect terms, opinion terms, and their corresponding sentiment polarity from text. ASTE enhances sentiment analysis by providing fine-grained insights into consumer feedback and social media discussions. Despite significant advances in ASTE, existing reviews largely focus on high-level sentiment analysis and lack a systematic categorization and synthesis of ASTE-specific methodologies. Therefore, this review aims to bridge this gap by systematically categorizing and comparing existing ASTE methods, assessing their applicability, and identifying their relative strengths and weaknesses in various scenarios. The review begins by outlining the evolution of ASTE methodologies, followed by a categorization of approaches based on technical advancements. It then summarizes the format, characteristics, and acquisition methods for datasets, including commonly used model evaluation metrics. Based on this analysis, the review identifies current limitations and proposes future research directions, such as improving model adaptability and robustness through domain adaptation, transfer learning, and leveraging large pre-trained models. Additionally, it suggests enhancing model interpretability through symbolic logic and causal reasoning. This review aims to guide researchers and practitioners by providing a comprehensive analysis of the progress, challenges, and opportunities in advancing ASTE technology.</p>