•Over 40 models for aspect-based sentiment analysis are summarized and classified.•Deep learning methods use fewer parameters but achieved comparative performance.•Deep learning is still in infancy, given challenges in data, domains and languages.•A task-combined and concept-centric approach should be considered in future studies. The increasing volume of user-generated content on the web has made sentiment analysis an important tool for the extraction of information about the human emotional state. A current research focus for sentiment analysis is the improvement of granularity at aspect level, representing two distinct aims: aspect extraction and sentiment classification of product reviews and sentiment classification of target-dependent tweets. Deep learning approaches have emerged as a prospect for achieving these aims with their ability to capture both syntactic and semantic features of text without requirements for high-level feature engineering, as is the case in earlier methods. In this article, we aim to provide a comparative review of deep learning for aspect-based sentiment analysis to place different approaches in context.