This paper describes Slav-NER: the 3rd Multilingual Named Entity Challenge in Slavic languages. The tasks involve recognizing mentions of named entities in Web documents, normalization of the names, and cross-lingual linking. The Challenge covers six languages and five entity types, and is organized as part of the 8th Balto-Slavic Natural Language Processing Workshop, co-located with the EACL 2021 Conference. Ten teams participated in the competition. Performance for the named entity recognition task reached 90% F-measure, much higher than reported in the first edition of the Challenge. Seven teams covered all six languages, and five teams participated in the cross-lingual entity linking task. Detailed valuation information is available on the shared task web page.