Hundreds of years after it was first used, the monoalphabetic substitution cipher was still thought to be unbreakable. In the ninth century, the eastern Islamic countries were lead the world for literacy and knowledge, and it was here that the cipher was broken, using a method called frequency analysis.
This seems almost obvious nowadays, but at the time it was the greatest breakthrough in cryptanalysis (the art of breaking encrypted code). The easiest way to explain it is to look at a paragraph coded with the monoalphabetic substitution cipher.
Using the frequency analysis system and a little bit of educated guesswork, we have successfully translated the code into the original text, and in doing so, have found the key used for encryption. It takes a while to do - longer than decryption using the key to start with - but not long enough to ensure privacy for the people using the code. If I send my friend Paul a letter coded this way telling him to sneak out and come to the pub this evening, his mother could copy it in the morning when she checks his post, and have deciphered it soon enough to stop Paul going to the pub and make him do some work instead. So now Paul's mother has the upper hand, and Paul and I need a new method to code our meeting plans.