Every year, the Conference on Computational Natural Language Learning (CoNLL) features a shared task, in which participants train and test their learning systems on the same data sets. In 2018, one of two tasks was devoted to learning dependency parsers for a large number of languages, in a real-world setting without any gold-standard annotation on test input. All test sets followed a unified annotation scheme, namely that of Universal Dependencies. This shared task constitutes a 2nd edition—the first one took place in 2017 (Zeman et al., 2017); the main metric from 2017 has been kept, allowing for easy comparison, also in 2018, and two new main metrics have been used. New datasets added to the Universal Dependencies collection between mid-2017 and the spring of 2018 have contributed to increased difficulty of the task this year. In this overview paper, we define the task and the updated evaluation methodology, describe data preparation, report and analyze the main results, and provide a brief categorization of the different approaches of the participating systems.