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Phenomenon of the children’s talent is one of the most important aspects amongst the main global problems of the contemporary education. Therefore, all questions related to identification, support and further development of the talented children and the talented young people are subject of an utmost attention due to the fact that both categories are the main intellectual human asset of any country of the world. There are various pedagogical methods and technologies of development of the talented children and teenagers. One of the most effective is considered to be involvement of the schoolchildren into various subject olympiads and competitions. There can be distinguished the following methods of research of the problems related to the talented students support by means of development of olympiad movement: analysis, comparison, generalization of the innovative pedagogical experience, observations, discussions with the schoolchildren and the teachers. Practical experience of the Republican Olympiad center in Tatarstan presented in the Article proves efficiency of the training sessions conducted at its premises with involvement of the teachers from the Universities as consultants and trainers as well as the seminars, round tables and training sessions with the mentors of the participants of the final stage of All-Russian Olympiad on technology: effectiveness, presented in 2016 by the team of the students of Republic of Tatarstan was higher than in 2015 by 25% and higher than in 2014 by 62,5%.