What is Imperialism? The definition of Imperialism is, "A policy of extending a country's power and influence through diplomacy and force." A simpler way to put is a stronger country takes over a weaker country.
During the Imperialism era, Europe was heavily involved. The three factors that motivated the European Imperialist push in Africa were economic, political, and social. There was a huge scramble to colonize in Africa that people feared it might lead to wars.
There was British Imperialism involved with China. The main motive was because of economic reasons. There was a high demand for Chinese goods in the British markets. However Britain did not have enough silver to trade with the Qing Empire. Clashes between the two governments broke out and led into the Opium wars. As a result England was given the island of Hong Kong and trading rights in its ports.
Hawaii and Samoa were both taken over by the United States. The reason the U.S. wanted Hawaii was because they were deeply involved with a sugar trade. The U.S. wanted Samoa because they saw it as an important link in the south pacific. These islands were officially annexed into the U.S. in 1898 and 1899.
The United States taking Puerto Rico is another example of Imperialism. The U.S. saw Puerto Rico as an important economic region and they sought a key naval base on the island. Puerto Rico has yet to become a state but is under all U.S. federal laws.