Opinion summarisation is concerned with generating structured summaries of multiple opinions in order to provide insightful knowledge to end users. We present the Aspect Discovery for OPinion Summarisation (ADOPS) methodology, which is aimed at generating explainable and structured opinion summaries. ADOPS is built upon aspect-based sentiment analysis methods based on deep learning and Subgroup Discovery techniques. The resultant opinion summaries are presented as interesting rules, which summarise in explainable terms for humans the state of the opinion about the aspects of a specific entity. We annotate and release a new dataset of opinions about a single entity on the restaurant review domain for assessing the ADOPS methodology, and we call it ORCo. The results show that ADOPS is able to generate interesting rules with high values of support and confidence, which provide explainable and insightful knowledge about the state of the opinion of a certain entity. •We present a novel methodology for aspect-based opinion summarisation.•Our methodology combines deep learning and subgroup discovery methods.•We categorise the aspects of restaurant reviews and classify their opinion values.•The summaries are presented in explainable terms for humans as interesting rules.•We release a new dataset for assessing opinion summarisation models.