The Wade-Giles system of Romanisation of Chinese characters (rendering Chinese characters in Roman - i.e. western - letters) was devised in the nineteenth century and was the main method used for most of the twentieth century. In recent decades it has been replaced to a significant degree in popular use by the Pinyin system, devised by scholars in the People's Republic of China in the 1950s.
The system was first devised in 1859 by Sir Thomas Francis Wade (1818-1895), a British army officer who had served in the first Opium War (1839-42) and who in 1845 became a student interpreter in China. The system was modified in 1892 by Herbert Giles (1845-1935) and acquired its double-barrelled name.
Among the drawbacks of the system are that pronunciation of certain consonants is only obvious to the initiated. In Wade-Giles, P is pronounced as the letter B; P' is P. Likewise K is pronounced J and K' is pronounced K Thus the place name transliterated at Peking was always intended be pronounced Be(i) Jing (as in the Pinyin Beijing)rather than Pea-king. These anomalies, and very many others, are not present in the Pinyin system which, for English-speakers at any rate, gives a much more accurate version of the Chinese words.
But some characteristics of Wade-Giles have notable advantages. A single letter is used as the basis for pairs of phonemes that differ only in aspiration. This more accurately represents how Chinese treats these pairs, from a phonological perspective (in terms of which vowels and consonants with which they can co-occur). Wade-Giles is more linguistically accurate than Pinyin, which uses different basic symbols for these phoneme pairs. In many cases, the orthography used by Wade-Giles for diphthongs is also more phonetically accurate than the pinyin alternative. Consequently, many linguists prefer to use Wade-Giles rather than Pinyin. It is also often used in Chinese colleges and universities to transition students to English.