In my view, the best source to consult on this is C.L.R. James's The Black Jacobins. Please pay particular attention to the first chapter, "The Property."
James uses the lectures of the late anthropologist and African scholar Emil Torday to assess the violence wrought on African societies by the Atlantic slave trade. He posits that, according to Torday, "in the sixteenth century, Central Africa was a territory of peace and happy civilisation [sic]" (James 7). Other historical sources, including John Hope Franklin's From Slavery to Freedom, place the beginning of the slave trade in the early fifteenth century. However, demand for slaves was not as high at this time due to the plentiful cheap labor offered by British indentured servants at this time.
James discredits historical revisionists who claim to have rescued Africans from tribal warfare by bringing them to the New World. He also counters those who cite systems of slavery which existed in West and Central Africa to excuse or diminish the inhumanity of the Atlantic slave trade: "It was on a peasantry in many respects superior to the serfs in large areas of Europe, that the slave-trade fell" (James 7).
The strongest and healthiest men and women were sold to European traders. This was the likely cause of tribal life being "broken up," resulting in "millions of detribalised [sic] Africans [being] let loose upon each other" (James 7). The destruction of communities allowed for recklessness. Violence and ferocity survived due to weakened tribes and poor leadership. The horrors did not end there:
The unceasing destruction of crops led to cannibalism; the captive women became concubines and degraded the status of the wife. Tribes had to supply slaves or be sold as slaves themselves (7).
With that last sentence, James takes on a more sympathetic view of decisions made by tribal chiefs and kings. Recent historians, such as Henry Louis Gates, Jr., have been more critical. Arguably, the truth is somewhere in between. Certainly, there were those who were blinded by greed, who coveted the gold and guns that European traders brought in exchange for human chattel. However, as James argues, there were probably also those who feared the Europeans' navies and weaponry -- those who offered men, women, and children not out of cruel avarice but for survival.
The United States and Great Britain ended the African slave trade in 1807, though slaves continued to be traded throughout the British colonies and in the United States. Other European countries, such as Spain, continued to kidnap and import slaves to their colonies, though some shipments were derailed by British navies.
Despite the end of the slave trade early in the nineteenth century, the exploitation of Africa -- this time, all over the continent -- would continue during the Age of Imperialism. By the 1870s, European nations, particularly Britain, began exploring Africa for mineral resources which would help fuel and supply their industries. The Berlin Conference of 1884-85, also known as the West Africa Conference or the Congo Conference, regulated colonization between European nations (i.e., allowed nations to divide Africa according to their own industrial needs), and helped lead to the emergence of Germany as a colonial power.
While it is certainly true that the African slave trade greatly diminished African societies -- some, according to James, as far south as Mozambique -- the exploitation of the continent did not end there.
Source: James, C.L.R. The Black Jacobins. New York: Vintage Books. 1989. Print.