The topic of simplified vs. traditional Chinese characters can be confusing if you are new to the Chinese language. The difference between these two written forms of Chinese is not to be confused with the difference between the Chinese dialects of Mandarin and Cantonese: both can basically be written in either simplified or traditional characters.
Traditional Chinese script has developed over many centuries of time. As characters became more complicated, informal forms of writing certain characters emerged. Simplified Chinese was introduced by the Mainland Chinese government in 1958 (with some slight changes over the years). It took the traditional Chinese characters and santioned some of the ‘shorthands’ while simplifying other characters that did not have a shorthand. “Only” some 500 characters were simplified; the rest have remained exactly the same between traditional and simplified Chinese.
The objective of this simplification exercise was to increase literacy by making it easier to write often used or very complicated characters. Whether this objective was really achieved remains the subject of debate. Some forces in the Chinese government have advocated to abolish the character script altogether and move toward only using Hanyu Pinyin as a writing method, but this proved unsuccessful. After going through many changes in the past decades, the Chinese government is wary of making any more changes, and it is thus not likely that Chinese characters are abolished any time soon.
Who uses what?
The People’s Republic of China uses simplified script and this script was also adopted by Singapore and Malaysia. Hong Kong, Macao and Taiwan use the traditional script. Internationally, traditional script is more frequently used with overseas Chinese. Language teaching used to take place mostly in traditional script until the 1980′s, if only because at that time, the People’s Republic of China was still very closed and most Chinese teachers originated from Taiwan. With China’s emergence, simplified Chinese has become the most popular script for learning Mandarin as a foreign language. A very detailed description of the usage can be found on Wikipedia.
Why not just one writing method?
My guess is that this has a lot to do with heritage, pride and national identity. As simplified Chinese was introduced by the communist party of China, it would be unlikely that Taiwan would adopt this script. Taiwanese will point out that the traditional characters are ‘ideographs’ which are like stylized pictures are easier to remember. A mainland Chinese might counter that it’s really easier not to have to remember so many strokes. Since the usage of language is moving towards computer typing, the complexity of characters may become less important.
Is it possible read and write traditional Chinese characters if you learnt simplified, and vice versa?
I am personally learning Mandarin based on the simplified script, and must say that it isn’t all that difficult to get the gist of a traditional text if you can read simplified. You need to learn a number of extra characters, and that’s about it. Most Chinese, be them in Hong Kong, China, or Taiwan, will be able to handle texts in the other script to some extent without formal teaching, though they’ll be more familiar with the script that they were taught in school and may not be able to write it.
While most simplified characters have a direct traditional equivalent, it is not exactly a one-to-one translation, i.e. there are exceptions, for example where several traditional characters are represented by one simplified character. So while there are computer programs that convert between traditional and simplified texts, they would need to be checked by a human afterwards.