The axion remains one of the most compelling hypothetical particles in modern fundamental physics, motivated originally as a solution to the strong charge–parity problem in quantum chromodynamics and subsequently emerging as a prime candidate for physics beyond the Standard Model and for non-baryonic dark matter. Over the past four decades, the theoretical axion parameter space has been reshaped by advances in particle theory, cosmology, and astrophysics, while experimental efforts have diversified into haloscopes, helioscopes, laboratory searches, and astrophysical probes. Among these, axion helioscopes occupy a unique position by directly targeting solar axions produced in the core of the Sun through well-understood plasma processes. This article presents a comprehensive and theoretically grounded examination of the development of axion helioscope science, tracing its evolution from early conceptual proposals to the current international effort embodied by the International Axion Observatory and its intermediate stage, BabyIAXO. By synthesizing insights from axion theory, solar physics, detector technology, X-ray astronomy, and large-scale instrumentation, this work elaborates on the scientific rationale, methodological frameworks, and experimental strategies that define the helioscope approach. Particular attention is given to the redefinition of the axion parameter window, the role of astrophysical constraints, the technological lineage from pioneering experiments to next-generation facilities, and the integration of precision X-ray optics and ultra-low background detectors. Through extensive theoretical elaboration and critical discussion, this article clarifies how IAXO represents not merely an incremental improvement, but a qualitative leap in sensitivity and discovery potential. The broader implications for particle physics, astrophysics, and cosmology are examined, alongside remaining challenges and future directions for axion research in the coming decades