The RuNNE Shared Task approaches the problem of nested named entity recognition. The annotation schema is designed in such a way, that an entity may partially overlap or even be nested into another entity. This way, the named entity "The Yermolova Theatre" of type ORGANIZATION houses another entity "Yermolova" of type PERSON. We adopt the Russian NEREL dataset (Loukachevitch et al., 2021) for the RuNNE Shared Task. NEREL comprises news texts written in the Russian language and collected from the Wikinews portal. The annotation schema includes 29 entity types. The nestedness of named entities in NEREL reaches up to six levels. The RuNNE Shared Task explores two setups. (i) In the general setup all entities occur more or less with the same frequency. (ii) In the few-shot setup the majority of entity types occur often in the training set. However, some of the entity types are have lower frequency, being thus challenging to recognize. In the test set the frequency of all entity types is even.This paper reports on the results of the RuNNE Shared Task. Overall the shared task has received 156 submissions from nine teams. Half of the submissions outperform a straightforward BERT-based baseline in both setups. This paper overviews the shared task setup and discusses the submitted systems, discovering meaning insights for the problem of nested NER. The links to the evaluation platform and the data from the shared task are available in our github repository.