The Second Opium War or Arrow War was a war of the United Kingdom and France against the Qing Dynasty of China from 1856 to 1860.

Background
The war may be viewed as a continuation of the First Opium War (1839-1842), thus the title of the Second Opium War.
On 1856-10-08, Qing officials boarded the Arrow, a Chinese-owned ship that had been registered in Hong Kong and was suspected of piracy and smuggling. Twelve Chinese subjects were arrested and imprisoned. The British officials in Guangzhou demanded the release of the sailors, claiming that because the ship had recently been British-registered, it was protected under the Treaty of Nanjing. Only when this was shown to be a weak argument did the British insist that the Arrow had been flying a British ensign and that the Qing soldiers had insulted the flag. Faced with fighting the Taiping Rebellion, the Qing government was in no position to resist the West militarily. This has come to be known as the "Arrow Incident".
The British Parliament decided to seek redress from China based on the report about the "Arrow Incident" submitted by Harry Parkes, British Consul to Guangzhou. France, the USA, and Russia received requests from Britain to form an alliance. France joined the British action against China, prompted by the execution of a French missionary, Father August Chapdelaine ("Father Chapdelaine Incident"), by Chinese local authorities in Guangxi province. The USA and Russia sent envoys to Hong Kong to offer help to the British and French, though in the end they sent no military aid.
The British and the French joined forces under Admiral Sir Michael Seymour. The British army led by Lord Elgin, and the French army led by Gros, attacked and occupied Guangzhou in late 1857. Ye Mingchen was captured, and Bo-gui, the governor of Guangdong, surrendered. A joint committee of the Alliance was formed. Bo-gui remained at his original post in order to maintain order on behalf of the victors. The British-French Alliance maintained control of Guangzhou for nearly four years. Ye Mingchen was exiled to Calcutta, India, where he starved himself to death.
The coalition then cruised north to briefly capture the Taku Forts near Tianjin in May, 1858.

Outbreak
In June 1858 the first part of the war ended with the Treaties of Tianjin, to which France, Russia, and the United States were party. These treaties opened eleven more ports to Western trade. The Chinese initially refused to ratify the treaties.
The major points of the treaty were:

Britain, France, Russia, and the United States would have the right to establish diplomatic legations (small embassies) in Peking (a closed city at the time)
Ten more Chinese ports would be opened for foreign trade, including Niuzhuang, Danshui, Hankou, and Nanjing
The right of all foreign vessels including commercial ships to navigate freely on the Yangtze River
The right of foreigners to travel in the internal regions of China, which had been formerly banned
China was to pay an indemnity to Britain and France in 2 million taels of silver each
China was to pay compensation to British merchants in 2 million taels of silver for destruction of their property Treaty of Aigun
In June 1858, shortly after the Qing Court agreed to the humiliating treaties, more hawkish ministers prevailed upon the Xianfeng Emperor to resist encroachment by the West. On June 2, 1858, the Xianfeng Emperor ordered the Mongolian general Sengge Rinchen to guard the Dagu Fort in Tianjin. Sengge Richen reinforced the Dagu Forts with added artillery. He also brought 4,000 Mongolian cavalry from Chahar and Suiyuan.
In June, 1859, a British naval force with 2,200 troops and 21 ships, under the command of Admiral Sir James Hope sailed north from Shanghai to Tianjin with newly-appointed Anglo-French envoys for the embassies in Beijing. They sailed to the mouth of the Hai River guarded by the Dagu Fort near Tianjin and demanded to continue inland to Beijing. Sengge Rinchen replied that the Anglo-French envoys may land up the coast at Beitang and proceed to Beijing but refused to allow armed troops to accompany them to the Chinese capital. The Anglo-French forces insisted landing at Dagu instead of Beitang and escorting the envoy to Beijing. On the night of June 24, 1859, a small batch of British forces blew up iron obstacles that the Chinese had placed in the Baihe River. The next day, the British forces sought to forcibly sail into the river, and shelled Dagu Fort. They encountered fierce resistance from Singge Rinchen's positions. After one day and one night's fighting, four gunboats were lost and two others severely damaged. The convoy withdrew under the cover of fire from a naval squadron commanded by Commodore Josiah Tattnall. Tattnall's intervention violated U.S. neutrality in China. For a time, anti-foreign resistance reached a crescendo within the Qing Court.
In the summer of 1860, a larger Anglo-French force (11,000 British, 6,700 French) with 173 ships sailed from Hong Kong and captured the port cities of Yantai and Dalian to seal the Bohai Gulf. Then they carried out a landing near at Bei Tang(also spelled Pei Tang), some 3 kilometres (2 mi) from the Dagu Fort on August 3, which they captured after three weeks' on August 21. After taking Tienstin on August 3, the Anglo-French forces marched inland toward Beijing. The Xianfeng Emperor then dispatched ministers to for peace talks, but relations broke down completely when a British diplomatic envoy, Harry Parkes, was arrested during negotiations on September 18. He and his small entourage were imprisoned and tortured (some were murdered by the Chinese in a fashion that infuriated British leadership upon discovery in October). The Anglo-French invasion clashed with Singge Rinchen's Mongolian cavalry on September 18 near Zhangjiawan before proceeding toward the outskirts of Beijing for a decisive battle in Tongzhou District. At Baliqiao, Sengge Rinchen's 10,000 troops including elite Mongolian cavalry were completely annhilated after several doomed frontal charges against concentrated firepower of the Anglo-French forces, which entered Beijing on October 6.
With the Qing army devastated, Emperor Xianfeng fled the capital, leaving his brother, Prince Gong, to be in charge of negotiations. Xianfeng first fled to the Summer Palace in Chengde and then to Jehol in Manchuria., as it was his own father, Thomas Bruce (1776–1841), who, from 1799 to 1803, removed from the Acropolis in Greece what are now known as the Elgin Marbles to Britain, where they remain to this day, a subject of rancor between the Greek and British governments.

Continuation of the war
After the Xianfeng emperor and his entourage fled Beijing, the June 1858 Treaty of Tianjin was finally ratified by the emperor's brother, Yixin, the Prince Gong, in the Convention of Peking on October 18, 1860, bringing The Second Opium War to an end.
The British, French and - thanks to the schemes of Ignatiev - the Russians were all granted a permanent diplomatic presence in Beijing (something the Qing resisted to the very end as it suggested equality between China and the European powers). The Chinese had to pay 8 million taels to Britain and France. Britain acquired Kowloon (next to Hong Kong). The opium trade was legalized and Christians were granted full civil rights, including the right to own property, and the right to evangelize.
The content of the Convention of Peking included:
Two weeks later, Ignatiev convinced the Manchu to sign a "Supplementary Treaty of Peking", in which the Manchu signed away some 300,000 to 400,000 square miles (777,000–1,036,000 km²) of land to the Russians. The defeat of the Imperial army by a small Anglo-French military force (outnumbered at least 10 to 1 by the Manchu army) coupled with the flight (and subsequent death) of the Emperor and the burning of the Summer Palace was a shocking blow to the once powerful Qing Dynasty. "Beyond any doubt, by 1860 the ancient civilization that was China had been thoroughly defeated and humiliated by the West."

China's recognition of the validity of the Treaty of Tianjin
Opening Tianjin as a trade port
Cede No.1 District of Kowloon (south of present day Boundary Street) to Britain
Freedom of religion established in China
British ships were allowed to carry indentured Chinese to the Americas
Indemnity to Britain and France increasing to 8 million taels of silver a piece
Legalization of the opium trade Further reading

Fraser, George MacDonald (1986). Flashman and the Dragon. New York, NY: Knopf. ISBN 0-394-55357-8.  — A portion of the memoirs of the fictional Harry Paget Flashman recounting his adventures during the Second Opium War and Taiping Rebellion.