Quantum computing is set to revolutionize numerous industries, including finance, healthcare, and cybersecurity, by harnessing the principles of quantum mechanics such as superposition, entanglement, and quantum tunneling. However, the advent of quantum computing also poses significant threats to traditional cryptographic methods, making them vulnerable to attacks that could potentially compromise global security and digital infrastructure. As quantum technology continues to advance, there is an urgent need to develop and implement quantum-resistant cryptographic techniques to safeguard sensitive data. This chapter explores the evolution of cryptography from classical to post-quantum methods, highlighting the current vulnerabilities in existing systems and the imperative for a global, coordinated effort to transition to quantum-safe standards. Through a detailed analysis of sector-specific challenges, case studies, and proposed solutions, the study underscores the necessity of strategic planning and international collaboration to address the emerging quantum threat. Future directions include advancements in quantum error correction, quantum key distribution, and the integration of quantum technologies with block chain, IoT, and AI, which are critical for building resilient cybersecurity frameworks in a quantum-dominated era.