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Résumé : This paper studies the theoretical foundations and observational prospects of soft hair and gravitational memory related to the quantum structure of black-hole horizons. It starts by putting the black-hole information paradox with its historical context, which outlines how classical general relativity and quantum mechanics rises to bright contradictions regarding unitarity and information conversation. Against this backdrop, the concept of soft hair, which is low energy excitations associated with asymptotic symmetries, emerges as a potential means of including and taking back information otherwise between soft theorems. The Bondi-Metzner-Sachs (BMS) symmetries, for example, highlights how these ideas manage to keep semiclassical gravity with quantum principles related logically. This study also solves observational solutions, especially how gravitational-wave astronomy could probe memory effects and horizon dynamics. Lastest detectors such as LIGO, Virgo, and NANOGrav makes linking theoretical predictions about soft modes to measurable signals achievable, which means it is possible to transform questions of principle into matter of empirical science. At last, this paper highlights the wider significance of soft hair and gravitational memory in shaping contemporary debates on the quantum science of spacetime by integrating theoretical arguments, historical development, and emerging data.