Radiomics research has been hindered by inconsistent and often poor methodological quality, limiting its potential for clinical translation. To address this challenge, the METhodological RadiomICs Score (METRICS) was recently introduced as a tool for systematically assessing study rigor. However, its effective application requires clearer guidance. The METRICS-E3 (Explanation and Elaboration with Examples) resource was developed by the European Society of Medical Imaging Informatics-Radiomics Auditing Group in response. This international initiative provides comprehensive support for users by offering detailed rationales, interpretive guidance, scoring recommendations, and illustrative examples for each METRICS item and condition. Each criterion includes positive examples from peer-reviewed, open-access studies and hypothetical negative examples. In total, the finalized METRICS-E3 includes over 200 examples. The complete resource is publicly available through an interactive website. CRITICAL RELEVANCE STATEMENT: METRICS-E3 offers deeper insights into each METRICS item and condition, providing concrete examples with accompanying commentary and recommendations to enhance the evaluation of methodological quality in radiomics research. KEY POINTS: As a complementary initiative to METRICS, METRICS-E3 is intended to support stakeholders in evaluating the methodological aspects of radiomics studies. In METRICS-E3, each METRICS item and condition is supplemented with interpretive guidance, positive literature-based examples, hypothetical negative examples, and scoring recommendations. The complete METRICS-E3 explanation and elaboration resource is accessible at its interactive website.