NSUCRYPTO is the unique cryptographic Olympiad offering scientific mathematical problems for professionals and students from any country. Its aim is to involve young researchers in solving curious and tough scientific problems of modern cryptography. From the very beginning, the concept of the Olympiad was not to focus on solving Olympic tasks but on including unsolved research problems at the intersection of mathematics and cryptography. In this talk, we would like to overview the history of the Olympiad, its modern trends, mathematical problems, and perspectives.