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Origins of the theory of formal languages and automata are surveyed starting from 1936 with the work of Turing and Post. Special attention is given to the machine translation projects of the 1950s and early 1960s and associated work in mathematical linguistics. The development of the Chomsky hierarchy of grammars, machines, and languages from 1956 to 1964 is traced. It is observed that the same important ideas emerged independently for the automatic analysis and translation of both natural and artificial languages. Since 1964, formal language theory is part of theoretical computer science. A few of the directions since 1964 are considered: restrictions and extensions of context-free grammars and pushdown store automata, unifying frameworks, and complexity questions.