Mathematical contests traditionally is an essential part of advanced education in Eastern Europe on middle and high school level. A great number of university teachers and research professionals are involved in them. A constant need for problems has resulted into bringing serious mathematical ideas and methods to ”contest curricula”. From the other side, there are mathematical ideas which were explicitly formulated at first in the ”contest area”. Also some serious investigations were originated by olympiad problems and accomplished by quite elementary methods. This ”border area” has been reflected in advanced textbooks for high school, resulting into serious improvement of mathematical education. Examples, trends, mathematical background and social consequences of these processes are reflected in the lecture.