The Malayalam script is used in Kerala, the southernmost province on India’s western shore. Kerala has been a destination for trade and travellers for thousands of years; Kerala is the easternmost point on the only surviving map of the Roman postal service, for example.
The script has had a long evolution, which makes assigning one date difficult. However, the evolution of the Malayalam script is punctuated with three significant events.
Background: The Malayalam spoken language was originally written in Vatteluttu. Like in the Tamil-speaking areas, most people moved to a hybrid of Grantha for for Sanskrit (in the Indo-European or Aryan language family), and Vatteluttu for the local language (in the Dravidian language family). This hybrid was commonly called Arya-eluttu.
First significant event: Around 1600 AD, the poet Thunchath Ezhuthachan wrote his poetry in the Malayalam language, but based on Sanskrit themes, using Arya-eluttu. When he needed a sound that was not in Arya-eluttu, he would use the Vatteluttu glyph. His poetry was wildly popular, and served to popularize the Arya-eluttu hybrid. It was not a perfect fit for the Malayalam language, as there were some distinctions that the script did not capture.
Second significant event: In around 1850 AD, a German missionary named Hermann Gundert published the first Malayalam-English dictionary, a Malayalam grammar, and a Malayalam translation of the Bible. Gundert also added a few new vowel diacritics to disambiguate the vowels, and they stuck. (This is the first time that I noticed that a foreigner made a change to a writing system that stuck!)
Third significant event: In 1969-1971 AD, the government reformed the script. In particular, they separated ligatures into independent glyphs. For example, diacritics which modified the vowel were subsequently written with two separate (non-conjoined) glyphs, the modifier to the right of the modified glyph. (Presumably this was to make printing with movable type easier.) They also eliminated some (but not all) consonant conjuncts.
Malayalam has a virama (called chandrakkala in Malayalam) to kill vowels, but also has six special consonants (called chillus) which never have a vowel following them. The chandrakkala is written above the consonant glyph, not to its right like the vowel diacritics; I guess there were limits to how much they were willing to reform the language in 1970 AD.
Malayalam, like Tamil, was written on palm leaves, which enforced a very curvaceous style. Like Tamil, it is a very pretty script.
Links: Technology Development for Indian Languages, Wikipedia, Omniglot, Ancient Scripts