We have selected problems that may not yet be well known, but have the potential to push the research in interesting directions. In particular, we state problems that do not require specific knowledge outside the standard circle of ideas in discrete geometry. Despite the relatively simple statements, these problems are related to current research and their solutions are likely to require new ideas and approaches. We have chosen problems from different fields to make this short paper attractive to a wide range of specialists.The article is published in the author’s wording.

Supported by the Russian government project 11.G34.31.0053. 2 Supported by the Russian government project 11.G34.31.0053. 3 Supported by the President's of Russian Federation grant NSh-581.2014.1, the Russian Foundation for Basic Research grant 13-01-00664, and the Russian government project 11.G34.31.0053. 4 Supported by the Russian government project 11.G34.31.0053. 5 Supported by the Russian government project 11.G34.31.0053.

We summarize the results of the First Yaroslavl Summer School on Discrete and Computational Geometry and asses its future perspectives.

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