Cryptography was introduced to prevent a third party from accessing and learning the contents of private messages sent during a communication process. Quantum Cryptography looks promising to provide a new level of secure communication by applying quantum mechanics concepts to cryptography. The research in the domain emphasizes that such systems can detect eavesdropping and ensure that it does not occur at all. This paper reviews the existing state of quantum cryptography, which includes an introduction to quantum computing and quantum key distribution algorithm, special attention is given to the implementation and working of the BB84 Protocol. It also provides a glimpse of post-quantum cryptography.