In recent years, significant progress in researching and building quantum computers has been made. A fully-fledged quantum computer would be able to efficiently solve a distinct set of mathematical problems like integer factorization and the discrete logarithm, which are the basis for a wide range of cryptographic schemes. In 2016, NIST announced an open competition with the goal of finding and standardizing suitable algorithms for quantum-resistant cryptography. The standardization effort by NIST is aimed at post-quantum secure KEMs and digital signatures. In this article, two of the to-be-standardized algorithms, Kyber and Dilithium, are presented and some of their mathematical details are outlined. Both algorithms are based on so-called lattices and the thereupon constructed »Learning with Errors«, which we will get to know in the following.