Aramaic is a North-West Semitic language, like Canaanite. Its name derives either from "Aram Naharayim" in Upper Mesopotamia or from "Aram", an ancient name for Syria. Various dialects of Aramaic coevolved with Hebrew throughout much of its history.
The language of the Neo-Babylonian Empire was a dialect of Aramaic. The Persian Empire that captured Babylonia a few decades later adopted Imperial Aramaic as the official international language of the Persian Empire. The Israelite population, who had been exiled to Babylon from Jerusalem and its surrounding region of Judah, were allowed to return to Jerusalem to establish a Persian province, usually called Judea. Thus Aramaic became the administrative language for Judea when dealing with the rest of Persian Empire.
The Aramaic script also evolved from the Canaanite script, but they diverged significantly. By the 1st century CE, the borrowed Aramaic script developed into the distinctive Hebrew square script (also known as Assyrian Script, Ktav Ashuri), extant in the Dead Sea Scrolls and similar to the script still in use today.
By the early half of the 20th century, modern scholars reached a nearly unanimous opinion that Aramaic became a spoken language in the land of Israel by the start of Israel's Hellenistic Period in the 4th century BCE, and thus Hebrew ceased to function as a spoken language around the same time. However, during the latter half of the 20th century, accumulating archeological evidence and especially linguistic analysis of the Dead Sea Scrolls has qualified the previous consensus. Alongside Aramaic, Hebrew also flourished as a living spoken language. Hebrew flourished until near the end of the Roman Period, when it continued on as a literary language by the Byzantine Period in the 4th century CE.
The exact roles of Aramaic and Hebrew remain hotly debated. A trilingual scenario has been proposed for the land of Israel. Hebrew functioned as the local mother tongue, Aramaic functioned as the international language with the rest of the Mideast, and eventually Greek functioned as another international language with the eastern areas of the Roman Empire. Communities of Jews (and non-Jews) are known, who immigrated to Judea from these other lands and continued to speak Aramaic or Greek.
Although the survival of Hebrew as a spoken language until the Byzantine Period is well-known among Hebrew linguists, there remains a lag in awareness among some historians who do not necessarily keep up-to-speed with linguistic research and rely on outdated scholarship. Nevertheless, current understandings of the vigor of Hebrew are slowly but surely making their way through the academic literature. The Hebrew of the Dead Sea Scrolls distinguishes the Dead Sea Scroll Hebrew from the various dialects of Biblical Hebrew out of which it evolved: "This book presents the specific features of DSS Hebrew, emphasizing deviations from classical BH." The Oxford Dictionary of the Christian Church which once said, in 1958 in its first edition, that Hebrew "ceased to be a spoken language around the fourth century BC", now says, in 1997 in its third edition, that Hebrew "continued to be used as a spoken and written language in the New Testament period". An Introductory Grammar of Rabbinic Hebrew says, "It is generally believed that the Dead Sea Scrolls, specifically the Copper Scroll and also the Bar Kokhba letters, have furnished clear evidence of the popular character of MH [Mishnaic Hebrew]." And so on. Israeli scholars now tend to take it for granted that Hebrew as a spoken language is a feature of Judea's Roman Period.
The international language of Aramaic radiated into various regional dialects. In and around Judea, various dialects of Old Western Aramaic emerged, including the Jewish dialect of Old Judean Aramaic during the Roman Period. Josephus Flavius initially wrote and published his book Jewish War in Old Judean Aramaic but later translated it into Koine Greek to publish it for the Roman imperial court. Unfortunately Josephus's Aramaic version does not survive.
Following the destruction of Jerusalem and the Second Temple in 70 CE, the Jews gradually began to disperse from Jerusalem to foreign countries, especially after the Bar Kokhba War in 135 CE when the Romans turned Jerusalem into a pagan city named Aelia Capitolina.
After the Bar Kokhba War in the 2nd century CE, the Jewish Palestinian Aramaic dialect emerged from obscurity out of the vicinity of Galilee to form one of the main dialects in the Western branch of Middle Aramaic. The Jerusalem Talmud (by the 5th century) used this Jewish Palestinian Aramaic, as did the Midrash Rabba (6th to 12th century). This dialect probably influenced the pronunciation of the 8th-century Tiberian Hebrew that vocalizes the Hebrew Bible.
Meanwhile over in Babylon, the Babylonian Talmud (by the 7th century) used Jewish Middle Babylonian Aramaic, a Jewish dialect in the Eastern branch of Middle Aramaic. For centuries Jewish Babylonian remained the spoken language of Mesopotamian Jews and the Lishana Deni. In the area of Kurdistan, there is a modern Aramaic dialect descending from it that is still spoken by a few thousand Jews (and non-Jews), though it has largely given way to Arabic.
Hebrew continues to strongly influence all these various Jewish dialects of Aramaic.