Aspect-based sentiment analysis (ABSA) is currently among the most vigorous areas in natural language processing (NLP). Individuals, private and government institutions are increasingly using media sources for decision making. In the last decade, aspect extraction has been the most essential phase of sentiment analysis (SA) to conduct an abridged sentiment classification. However, previous studies on sentiment analysis mostly focused on explicit aspects extraction with limited work on implicit aspects. To the best of our knowledge, this is the first systematic review that covers implicit, explicit, and the combination of both implicit and explicit aspect extractions. Therefore, this systematic review has been conducted to, 1) identify techniques used for extracting implicit, explicit, or both implicit and explicit aspects; 2) analyze the various evaluation metrics, data domains, and languages involved in the implicit and explicit aspect extraction in sentiment analysis from years 2008 to 2019; 3) identify the key challenges associated with the techniques based on the result of a comprehensive comparative analysis; and finally, 4) highlight the feasible opportunities for future research directions. This review can be used to assist novice and prominent researchers to understand the concept of both implicit and explicit aspect extractions in aspect-based sentiment analysis domain.