Highly controversial language "super-family" that putatively links as many as eight different language families (Indo-European, Dravidian, Mongolian, South Caucasian, Tungusic, Turkic, Uralic, and perhaps Afro-Asiatic).
In order to understand the idea of Nostratic languages, a quick precis of the concepts behind the discovery, methods of investigation, and application of the Indo-European family of languages is needed.
When Sir William Jones first suggested the Indo-European hypothesis, he backed up his idea with a systematic examination of what might be termed "phono-semantic sets" -- words which, in different languages, had both similar sounds and meanings. Jones essentially argued that there were too many of these sets for their existence to be mere coincidence. He proposed that the languages in question must have stemmed from one language at some time in the past, and that they diverged from one another due to geographical separation and the passage of time. The idea of a "root language" thus took hold.
The second major concept to keep in mind is that, starting with Jacob Grimm (of fairy tale fame), it was argued that languages would not evolve in a haphazard manner; that they evolved according to certain rules. Using these rules, one could theoretically run the evolutionary process backwards and reconstruct the root language. This has been done, and a hypothetical language named Proto-Indo-European has been produced.
The third concept is that, by analyzing the words in Proto-Indo-European language, one can to some extent examine what was the time and place of the Proto-Indo-Europeans. Words for concepts and objects that were not familiar to these people would be named essentially randomly after the time when the languages began to split; only things they knew would produce phono-semantic sets in their successor languages. Proto-Indo-European is rich in words related to agriculture and animal husbandry, and to a plains-like landscape. From this, it has been plausibly argued that Proto-Indo-European was a living language some time from 4000-6000 BC, in the plains to the north of the Black Sea. (A measure of the difficulty of this task can be gained by realizing that some argue the reconstructed vocabulary of Proto-Indo-European suggests a northern Anatolian landscape, which is notably lacking in flat ground),
Altogether, the Indo-European hypothesis has been wildly successful, and naturally linguists have tried to apply the same general theory to a wide variety of other languages. Many languages, though not all, have been shown to be related to other languages, forming large families similar to Indo-European. However, these families have been as "high-level" as connections have been plausibly been made. Superficially, though, it is logical that the family tree could converge further, and that some or all language families could be related to one another.
Enter Nostratic. In 1931, the Danish linguist Holger Pedersen proposed "Nostratian", a proto-language for the proto-languages of the Indo-European, Uralic, Afro-Asiatic, and Eskimo-Aleut language families. The name derives from the Latin word noster, meaning "our". While the hypothesis did not make much headway in the West, it became quite popular in the Soviet Union, and under the slightly modified name "Nostratic" was expanded to include other language families.
Almost all modern linguists are, at best, highly skeptical of the facts put forward to show that the language families under the Nostratic umbrella are, in fact, related. Most of the proposed "phono-semantic sets" are much more speculative than those used to group languages into the accepted families -- one technique used to support a similar "super-family" was famously used in the 1960s to "demonstrate" that English was a member of a proposed Central American language family. Another blow against Nostratic is that the more recent technique of comparing grammatical structures, as opposed to words, suggests that the Nostratic candidates are not related. Claims that the words reconstructed for Proto-Nostratic point to a pre-agricultural society in the Middle East (as one might expect for a language pre-dating Proto-Indo-European) have been dismissed as wishful thinking exacerbated by that very expectation shaping the results.
Some linguists also object to the assumption that languages must ultimately all stem from one reconstructable root. It is known that unrelated languages in close geographical proximity can trade vocabulary, syntax, and other features, and it is suggested that the present-day "family" structure of languages may be an aberration. Advancing technology might allow one language to rapidly expand in geographic scope, as the people speaking it conquer their neighbours. This would then allow that one language to evolve into a family (in fact, it has been argued that Indo-European languages have spread as far as they have due to war-making advantages the domestication of the horse gave to one small group of Proto-Indo-European speakers). In the absence of rapid technological change, as was the case prior to about the eighth millennium BC, the tendency of languages to evolve would be drowned out by the tendency for languages to trade features between each other. If this were so, the axiom that languages change in a manner that can be reversed is not true before a certain point in the past, and it will not be possible to reconstruct older proto-languages, Nostratic or otherwise, using the techniques used to reconstruct the proto-languages of the accepted major language families (all of which are believed to post-date the invention of agriculture).
Regardless, the concept of Nostratic languages still has some influence on the fringes of linguistics. A further level of the "language family tree", which weds Nostratic with all other language families into what is called Proto-World, has been proposed. Most of the objections raised to the Nostratic hypothesis apply equally to this idea, and the Proto-World concept has little currency among linguists.