Despite being plagued by serious conceptual problems, underachievement ranks among the most popular constructs in research on the gifted. Many of its problems have their roots in the use of the IQ as the supposedly best method of measuring ability levels. Only a few decades ago the opinion was still widespread that the IQ-based construct of underachievement, having withstood neither its empirical nor its theoretical test, ought to be abandoned. Since then, some points of criticism have simply been forgotten. In this article we therefore take up and follow a few of the broken threads within the discussion. To this end, we present a thorough analysis of the implications of the IQ-based underachievement concept. First we present a definition of underachievement and provide a brief overview of the history of the construct. We then enumerate the theoretical, methodological, and empirical problems of the IQ-based construct. (Contains 1 table, 1 figure, and 1 note.)