Aspect-level sentiment analysis is crucial for consumers and institutions, enabling them to monitor satisfaction regarding specific aspects of products and services through user reviews. Over time, various artificial intelligence techniques have been implemented with significant success. However, most of these techniques rely heavily on a substantial amount of labeled data. In this context, Cross-Domain Aspect-Based Sentiment Analysis (ABSA) emerges, leveraging data from source domains to enhance performance in the target domain. This systematic review contributes to this framework by outlining the primary solutions developed to tackle this challenge. It presents their data sources, compared methods, and the evolution of the main technologies adopted while identifying gaps that may inspire future research endeavors. A new classification of models is proposed here, considering the cross-domain approach. This fresh perspective aims to assist researchers in their quest for innovation, clarifying the context of their proposal and suggesting relevant comparisons with existing works.