Quantum computing poses an unprecedented threat to the cryptographic foundations that secure our digital civilization! This paper presents a comprehensive examination of post-quantum cryptography (PQC), tracing the revolutionary transition from classical to quantum-resistant cryptographic systems. We analyse the mathematical foundations underlying major PQC families, including lattice-based, code-based, hash-based, multivariate, and isogeny-based approaches. The paper evaluates the groundbreaking NIST PQC standardization process and its transformative impact on cryptographic development, while examining implementation challenges across diverse platforms. Performance metrics and security analyses reveal the fascinating trade-offs between different approaches. We conclude by exploring emerging research directions and challenges in securing digital infrastructure against the quantum revolution.