1. Numerous attempts were made by many people, try to encode thousands of Chinese characters in keyboard. The most popular one is Wubi, which can describe single character in 4 keystroke so you don't need to select from options. It's used by professional typewriters, and many regular users spend a lot of time to learn the system.
2. pinyin IME was improved, provided better prediction and word input(input a multi character word directly, instead one by one), it's acceptable even you need to select from a list, and you don't need to learn a system. Most casual users used the one provided by Windows Chinese version.
3. Whole sentence IME appeared, which was trained with Chinese text corpus, try to predict a whole sentence when you just input the pinyin for all of them. This proved to be short-lived since you still need to adjust several places in many cases, even it can get 100% correct in 30% cases.
4. All major IT companies start to develop their own IME as a method to collect user input and provide an entrance to their product.
5. An old IME: double pinyin start to gain more popularity. It's still pinyin, but you can use 2 letter to encode the whole pinyin instead of 4 or 6 letters. All newer IME can switch between different encoding methods, like pinyin, double pinyin, strokes.
6. Senior users tend to just use handwriting in smartphone.