Twenty-five years after the introduction of Carroll's (1993) Three Stratum (3S) theory of intelligence and McGrew's (1997) subsequent synthesis of 3S with the extended Gf-Gc / Horn-Cattell theory, the Cattell-Horn-Carroll (CHC) theory represents the prevailing framework by which the structure of human cognitive and intellectual abilities is understood. This commentary reviews, discusses, and supplements the critical examinations of CHC theory appearing in this special issue of Applied Measurement in Education. After recounting the historical foundations and structural framework of CHC, a series of challenges to this theory are compiled including its weak explanatory capacity, its failure to make testable predictions, its enmeshment with a single measurement instrument (i.e., the Woodcock--Johnson), the inconsistent independent replication of its factor structure, and most importantly, its undemonstrated evidential value for identification and intervention with students with specific learning disorders (SLDs). The inherent limitations of any psychological theory developed or tested primarily from factor analyses are enumerated. Solutions are proposed to advance psychological science in areas related to CHC theory.