In this talk, we will give a brief survey on the importance of post-quantum cryptography by describing current approaches. Then, we will discuss the computationally hard problems used in post-quantum cryptographic schemes focusing on lattice-based and code-based cryptography. The focus will be given to the NIST Post-Quantum Cryptography Standardization Project in view of formal security and performance. We will also discuss the open problems in post-quantum cryptography.