National policy initiatives in Ireland, such as Project Maths and the Science, Technology, Engineering, and Mathematics (STEM) Education Policy Statement have sought to increase the engagement and performance of students in mathematics and science. The current study investigated the performance of students in Ireland in these areas and in reading in international large-scale assessments (Programme for International Student Assessment [PISA], Trends in International Mathematics and Science Study [TIMSS], and Progress in International Reading Literacy Study [PIRLS]), with a view to better understand the performance of high-achieving students, relative to their counterparts in other countries in general, and in countries with similar average performance. Lower than expected proportions of high achievers were noted and a pattern of relative underachievement was observed among high achievers -- those performing at the highest levels of proficiency, and those performing at key benchmarks, including the 75th and 90th percentiles -- in mathematics and science to a greater extent than in reading. These issues were found to be consistent over time, and more prevalent at post-primary level, compared with primary level. The findings of this study are discussed with reference to individual and societal costs, and specific issues that need to be investigated further are identified.