Shu Han never called itself Shu; the name was a rival's insult
Liu Bei's state in south-west China called itself simply Han, claiming to be the rightful continuation of the fallen Han dynasty. Its northern rival, Cao Wei, tacked on the regional label Shu to deny that claim, and the historians followed. For 42 years this smallest of the Three Kingdoms fought far above its weight.
Liu Bei was a warlord and distant relative of the Han imperial family. Following the Longzhong Plan of his adviser Zhuge Liang, he took parts of Jing Province in 208 and 209, seized Yi Province, roughly modern Sichuan and Chongqing, between 212 and 214, and wrested Hanzhong from Cao Cao in 219. That same year his ally Sun Quan turned on him, took Jing Province and executed his general Guan Yu. When Cao Cao's son Cao Pi forced the last Han emperor to abdicate in 220, Liu Bei answered by declaring himself Emperor of Han in 221.
His reign lasted under three years. Seeking to recover Jing and avenge Guan Yu, he was routed by Sun Quan's general Lu Xun at Xiaoting and died of illness a year later. His son Liu Shan took the throne at 16, the youngest ruler of the three states, while Zhuge Liang ran the government in practice. Hemmed in with a small population, Shu could defend itself but struggled to attack, so Zhuge Liang restored the alliance with Wu and pacified the southern region of Nanzhong in 225.
Convinced that survival demanded offence, Zhuge Liang led five campaigns against Wei between 228 and 234, aiming at Chang'an; they won the officer Jiang Wei and two commanderies but little else, and Zhuge Liang died, worn out, during a stalemate against Sima Yi. Shu later beat an invasion at Xingshi in 244 despite being outnumbered two to one. Jiang Wei's further offensives from 247 exhausted the state, and in 263 Wei armies took Chengdu with little resistance. Liu Shan surrendered and lived out his days comfortably as Duke of Anle.
Peace left a legacy too: Shu built roads and irrigation that helped launch Sichuan's economy, and some of those works, such as the Zipingpu Dam near Chengdu, remain in use.
Source: Shu Han