Universal Dependencies (UD) is a project that seeks to find a cross-linguistically applicable morphological and syntactic annotation scheme, and to publish data conforming to that scheme in a wide range of languages. We will briefly motivate and introduce the project, its history and underlying principles. Then we will present the new proposal of version 2 UD guidelines. Finally, time permitting, we will describe several interesting problems related to the application of UD to Slavic languages.