Transliterations have existed since at least the 19th century, most notably with the Wade Giles system.
Now though Pinyin is the international standard, and is how mainland schools teach pronunciation.
Taiwanese still uses Zhuyin, but in recent years the government has adopted Pinyin for street and city naming.
(I'm not sure if schools are still teaching zhuyin, but friends in their 20s don't know pinyin).
I live and grew up in Taiwan. Zhuyin is a learning tool taught to all schoolchildren to teach pronunciation. It also happens to be a computer input method because everyone knows it, and the alphabet fits onto a computer keyboard. No adult regularly uses Zhuyin otherwise.
I've recently switched to using Pinyin for computer input because Zhuyin has a larger alphabet compared to Pinyin, and the Zhuyin keyboard on iOS has smaller keys to fit more characters in the same space, making it much harder to type with. The Pinyin keyboard is essentially an English keyboard that spits out Chinese.
Well sure, but I've found these kinds of systems, and the number of different systems, difficult to use. Latin just isn't a very good alphabet, even for English. I deal with Koreans more and I always find it better to just see the Hangul than whichever transliteration system of the day is in use because trying to shoehorn vowels and consonants that simply don't exist in Latin into Latin is a tough battle.
Zhuyin has the nice aspect of properly representing the spoken language and isn't hard to learn, probably a couple weeks of an hour or two a day and you'll be able to pronounce most things.
Now though Pinyin is the international standard, and is how mainland schools teach pronunciation.
Taiwanese still uses Zhuyin, but in recent years the government has adopted Pinyin for street and city naming. (I'm not sure if schools are still teaching zhuyin, but friends in their 20s don't know pinyin).