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In the history of cryptography, le chiffre indéchiffrable (French for 'the unbreakable cypher') was long used to refer, confusedly and incorrectly, to either of two hand cyphers named after Blaise de Vigenère (ie, Vigenère cypher). One was misattributed to him, having been first described in 1553 by Giovan Batista Belaso. The other was actually invented by Vigenère and is an autokey cypher. Both are polyalphabetic substitution cyphers; neither is unbreakable.
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Cryptanalysis
Because the first mentioned is quite easy to use, it became both well known and widely used for several hundred years. Both were actually quite difficult to break until systematic methods were developed in the mid 1800s. Hence the long used epithet, 'unbreakable'. Both Charles Babbage, before the Crimean War, and Friedrich Kasiski, who published in 1863, found practical ways to attack polyalphabetic cyphers.
In 1917, the Vigenère was described as "impossible of translation" in the respected journal Scientific American.
Modern use
One of the Vigenère cyphers is usually an early exercise in introductory cryptography courses, as is its cryptanalysis. It is, therefore, unfortunate that software applications continue to sometimes use an embedded Vigenère cypher to protect user data. To developers who haven't taken cryptography courses, either of the Vigenère cyphers may still appear to be indechiffrable; at least the first is still (attractively) easy to implement. Variations on both have been discovered in modern day crypto systems.
Even though these types of cypher are easily broken, there are products which use them while claiming to have "good security" or "unbreakability" — see snake oil.
Actual unbreakability
During World War II, Claude Shannon of Bell Labs proved, mathematically, that the one-time pad cypher is unbreakable in a strong, though limited, sense. He further showed that any unbreakable encryption method will have certain properties, more or less the same as those of the one-time pad. He published an account of this work in the Bell Labs Technical Journal in 1948/49. Neither of the two cyphers here discussed is this strong.