The Qing Dynasty (1644-1911 C.E.) was the last Chinese Imperial dynasty (unless one accepts the slightly puckish claims of some historians that modern Communist rule should be considered the "Mao Dynasty"). It was the second major Chinese dynasty where the royal family was of non-Han descent, after the Mongol Yuan Dynasty; in this case they were Manchurians, which gives the dynasty its alternate title as the Manchu Dynasty.
Historical thought on the Qing is conflicted - on the one hand they held together a strong and prosperous central state and bureaucracy that maintained public works while keeping taxes relatively low, and presided over a cultural and artistic flowering, but on the other, their strong isolationism and resistance to government reform ultimately brought China to its knees, wracked by foreign domination and internal rebellion.
Modern scholarship and popular conception of the Qing has a certain, perhaps regrettable, tendency to focus on this later period of dissolution and indignity, especially the humiliating Opium Wars, to the exclusion of their earlier accomplishments. In particular, the current Chinese government tends to evoke images of this period as an example of why China must resist all attempts at foreign hegemonism (i.e., on the part of the United States).
The official life of the Qing, throughout the course of the dynasty, was marked by an extreme, arguably decadent, focus on protocol and formalism, no doubt prompted in part by the Manchurian Qing ruling class's mixed feelings about asssimilation into the dominant Han cultural milieu. The Qing set up two roughly parallel bureaucracies of Han and Manchu officials, with most real power being vested in the Manchus. They forced Chinese to alter their appearance and dress to Manchu fashions, attempted unsucessfully to restrict the practice of foot-binding, and adopted Tibetan Gelug ("Yellow Hat") Buddhism as the official state-supported religion.
As the power of the Qing waned, individual Emperors tended to be reduced to the status of expendable pawns of foreign governments, and tended to die younger and younger, usually as the result of foul play. The culmination of this trend was the coronation of Pu Yi, The Last Emperor (and subject of the excellent movie of the same name), at the ripe old age of three years, and his deposition two years later in 1911, at the time of the founding of the Chinese Republic.