Euro-Siberian is the name, suggested independently by Jan Strasser and Juho Pystynen (John Vertical), of a hypothetical language family proposed by Frederik Kortlandt and supported by Jörg Rhiemeier, consisting of Indo-European, Uralic, Yukaghir, Chukotko-Kamchatkan and Eskimo-Aleut.
Relationships between these languages have been suspected since the early 19th century. Rasmus Rask noticed similarities between Uralic and Eskimo languages, and Indo-Uralic also has a long-standing tradition, though it is not generally accepted yet. In 1998, Michael Fortescue, in his book Language Relations across Bering Strait, proposed a Uralo-Siberian stock consisting of Uralic, Yukaghir, Chukotko-Kamchatkan and Eskimo-Aleut. The Euro-Siberian hypothesis combines Uralo-Siberian with Indo-Uralic.
It is an open question (assuming, of course, that Euro-Siberian as such is valid) whether Uralic is more closely related to Indo-European (i.e., Indo-Uralic is a valid node) or more closely related to Yukaghir, Chukotko-Kamchatkan and Eskimo-Aleut (i.e., Uralo-Siberian is a valid node). Other topologies of the family tree (e.g., IE-Uralic-Yukaghir vs. CK-EA) are of course possible as well. The amount of lexical cognate candidates is similar in both directions. Most of the morphological elements shared by the "Uralo-Siberian" languages are also found in Indo-European, and most of those shared by Indo-European and Uralic are also found in at least one of the more easterly languages. The typology of the Uralic languages does not much to settle the issue, as the western Uralic languages are typologically more similar to Indo-European languages but the eastern ones more similar to Yukaghir, Chukotko-Kamchatkan and Eskimo-Aleut. In general, Uralic languages appear to be slightly closer to Indo-European than to the eastern languages.
The homeland of Proto-Euro-Siberian and the migration patterns of the hypothetical family are also an open question which is connected to the topology of the family tree. The geographical distances between the languages are considerable, with Indo-European and Uralic probably originating in eastern Europe (north of the Black Sea and between Volga River and Ural mountains, respectively), and the other languages in eastern Siberia. This geographical clustering perhaps supports the assumption that Indo-Uralic is a valid node and Uralic more closely related to Indo-European than to the eastern languages.
Distinct from Mitian?
The question remains whether Euro-Siberian is distinct from Mitian (in being a subgroup of the latter) or not. It is possible that "Euro-Siberian" is not a valid node within Mitian, but rather Mitian itself, if the Altaic languages descend from the same ancestor rather than forming a sister clade of Euro-Siberian. This is an issue of subgrouping within Mitian which still requires exploration.