Technically, Aramaics would be the people using an Aramaic language.
7th century BCE funerary stele from Such Afis, Syria. It has inscription in Aramaic, the male figure must have been shaped according to Aramaic patterns, and with ideal physical attributes. Note in particular the nose.
The peoples are, however, rather known as Assyrians, although categorizations like Chaldeans or Syriacs are also used.
Only a minority of the Assyrians speaks Aramaic today, the majority speaks Arabic.
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The ancient Aramaics emerge as one of several important Semitic peoples in the 2nd millennium BCE. Originally nomads, they established small kingdoms mainly in the lands corresponding to modern Syria, becoming active in the trade between the Hittite Empire and Assyria in the north and northeast, and Palestine and Egypt in the south and southwest.
What historical events made Aramaic the most important language in ancient Middle East remains a question unanswered. The historical and archaeological information is very insufficient.
What at least seems to have happened, and which may have been enough for victory of their language, is that politically, the Aramaics gradually replaced the Mitannis and the Hittites.