Aspect-based sentiment analysis (ABSA) has witnessed notable progress in recent years, driven by increasing interest in fine-grained sentiment elements and the emergence of more complex tasks. However, implicit sentiment, particularly in compound ABSA tasks such as sentiment triplet and quadruple extraction, remains underexplored, which hinders the development of robust, domain-adaptive ABSA solutions. To address this gap, we present a systematic literature review of 85 peer-reviewed studies from 2019–2024, categorizing them by task, learning paradigm, and application domain. To the best of our knowledge, this is the first survey to focus on implicit sentiment extraction across single and compound ABSA tasks. We identify key research trends and challenges, and outline future directions in prompt-based modeling, cross-domain adaptation, and multimodal sentiment analysis. These insights are intended to support the development of more generalizable ABSA systems capable of effectively handling implicit sentiment.