Under British rule, Calcutta became a huge port that greatly benefited the economic situation in the region, including Bangladesh, as the Indian city sits on the Bengali-Indian border. Under this foreign rule, Bangladesh was just one of many provinces that were a part of British India. Bangladesh though was a very significant and powerful province, partially due to its location next to the British capital city of Calcutta.
Although Bangladesh prospered in many ways under British rule, the people sought independence as did many of their neighboring Indians. Throughout British India (which included present day Bangladesh, India, and Pakistan), independence movements arose during the late 1800s and continued into the 1900s.
Independence demands by the people of British India were divided. Some sought a single country once free, while others wanted a number of countries determined by religion, most notably the Muslims, who feared Hindu domination in a shared state. In 1947 the country was given independence in the form of India and Pakistan, with modern day Bangladesh making up a part of Pakistan, then called "East Pakistan."
From the time of independence few issues seemed to be resolved as disagreements were rampant among the people of Bangladesh as well as issues with the central Pakistan government, which was incredibly far away. Among these issues, the central Pakistan government wouldn't recognize Bengali as an official language (with the Pakistani language of Urdu being the only official language at the time). This, among numerous other cultural-political issues led to the Bengalis demanding independence from Pakistan.
In 1970, after gaining nearly full local support for independence, Pakistan still refused to grant Bangladesh independence, leading to the presence of more Pakistani troops in Bangladesh to prevent violence and war, while the Bengalis escalated their independence demands in the form of speeches, rallies, and acts of defiance. India stepped in in December of 1971 in order to assist the Bengalis, as they had strained relations with Pakistan's central government. With this assistance, Bangladesh gained independence in 1971.
Immediately after independence little progress took place in Bangladesh as the economy struggled and the government was riddled with coups or assassinations through the early 1980s, when the military took control of the government. After they nominally released this power politics settled, although corruption in these elections seemed to continue as many opposition parties claimed that the military still ruled the country.
Since this time numerous parties have regularly boycotted elections with the belief that they are unfair and rigged, but in 1996 international observers claimed the elections, for the first time in Bangladesh were free and fair. This led to greater political involvement, but protests and election boycotts by numerous parties has continued to the present.
Since about 2000 Islamic extremists have also made headway in Bangladesh, but with little support. This has only encouraged more political instability in the country, which still seems to undergo a coup or protest annually.