Aspect-based sentiment analysis (ABSA) is one of the principal tasks in the automatic deep understanding of texts, widely applied in a broad range of real-world applications. Many studies have been performed on different tasks and datasets for other languages (e.g., English, Chinese) to address this topic. For Vietnamese language, this topic has been attracting considerable interest in recent years. However, we found that many studies tend to repeat the research instead of inheriting and extending the previous works. Moreover, previous studies’ methods of comparison or evaluation metrics have not shown consistency and connection. This might restrict the development of future studies on this research topic. To the best of our knowledge, no research has been conducted to overview the existing studies for the ABSA research in Vietnamese language. The primary objective of this study is to provide a systematic and comprehensive review of the current Vietnamese ABSA research. More specifically, we analyze the early approaches, evaluation metrics, and available published benchmark datasets used in the Vietnamese ABSA task. We also discuss the challenge and recommend potential future directions for Vietnamese ABSA. This work is expected to provide readers with a wealth of knowledge, the research gap, and the challenges in the Vietnamese ABSA field.