Gwoyeu Romatzyh

Gwoyeu Romatzyh (pinyin: "Guóyǔ luómǎzì", literally "National Language Romanization"), abbreviated GR, is a romanization of Mandarin Chinese, or a way to write Mandarin using the Roman alphabet, made by Yuen Ren Chao and some other linguists in the late 1920s. It was made as a way to write Mandarin using tonal spelling, or spelling rules that would change the syllable's spelling depending on its tone. For example, the syllable "chai" would be written as "chai" if it has the first Mandarin tone (or "chāi" in Pinyin), "chair" if it has the second tone ("chái")", chae" if it has the third tone ("chǎi")"," and "chay" if it had the fourth tone (chài). Y.R. Chao created GR in order to increase literacy in China because China's illiteracy was very high in the early 20th century. He made it that tones could be written without extra tone markers, which can be long and difficult to add when printing. 
Even though many other Asian languages use tonal spelling, like Hmong, they all represent tones by using the same letter each time the tone is used. In Hmong, for example, "-b is always" a high tone, "-s" is always a low tone, "-j" is always high-falling tone. In GR, however, each syllable final has its own spelling rules, and many exceptions exist within these rules. For example, first tone words with the final "-a" as in "bā" is written with just one vowel like "ba", except when the syllable begins with an "l-, m-," or "n-", which then must be written as "lha, mha," and "nha" in that order. This is only one of its many rules and exceptions. 
Unsurprisingly, many people thought GR was too difficult to learn. Nonetheless, it still has many supporters, and they would rather learn using GR than Pinyin. While supporters of GR claim that it helps users of GR remember tones better than people who just use Pinyin, studies have not supported this claim. As a matter of fact, one study showed that after one year, the subjects who learned Chinese using Pinyin could more accurately speak Mandarin with tones than those who learned using GR. 
After the Communist Party took over China, it tried to replaced all romanizations of Chinese, including GR, with Pinyin. While GR is not an official romanization in Taiwan, it can be seen in several places, including road signs, people's names, and the names of products, even though Hanyu Pinyin is the official romanization of Taiwan. 
Even though almost all romanizations in mainland China today are in Pinyin, there are still some exceptions. For example, the name of the province Shaanxi is written in GR rather than in Pinyin, which would be Shǎnxī with tone markers, because there is already another province named Shanxi, which is written as Shānxī with tones. If the Pinyin names were to be written without tone markers (which they often are in everyday Pinyin), they should both be spelled Shanxi. Therefore they would be impossible to tell apart using just Pinyin without tones. Therefore, an exception has been made in this case. 
Below are examples of sentences written in Chinese characters, Pinyin, and GR with English translations.