High achievement at school is considered to be a strong predictor of students’ professional and social success, and of a country’s economic development. High achievement in mathematics and science, in particular, has been linked to building a knowledge society and driving sustainable economic growth, while also delivering social recovery. In Ireland, while, on average, students have performed well on national and international assessments of mathematics and science, the low proportions of high achievers in these subjects are noteworthy. In response, this study conducted an in-depth investigation of high achievement across education levels, student cohorts, and subjects using data from the Programme for International Student Assessment (PISA), the Trends in International Mathematics and Science Study (TIMSS), the Progress in International Reading Literacy Study (PIRLS), the Irish National Assessments, and the Irish state examinations (Junior and Leaving Certificates). The study aimed to (i) examine the magnitude and consistency of the issues related to high achievement in Ireland, (ii) build profiles of high-achieving students, and (iii) evaluate the contribution of various contextual characteristics in the prediction of high achievement in mathematics and science in a multivariate and multilevel context. The findings indicated that Ireland’s percentages of high achievers and scores among students at the highest national percentiles of performance in mathematics and science have been significantly lower compared to countries with similar average performance. These issues, which were consistent across years and assessments, were more apparent for mathematics than science and at post-primary than at primary level, while similar patterns were not detected for reading. It was also found that variables related to students’ self-beliefs, dispositions, engagement, learning approaches, and socioeconomic background were consistently associated with high achievement in mathematics and science. The implications of these findings for policy and practice, recommendations for future research, and the limitations of the study are discussed.