What areas were Europeans able to colonize?

Just to set things straight, Europe did not colonize any area collectively. This is because Europe is a continent made of many nations, who were in competition to get the most colonies. Europe had two ages of Imperialism: the first focused on the Americas while the second focused on Africa and Asia.

1st Age of Imperialism:

The main European countries who colonized the Americas were Spain, France, Great Britain, Portugal, and the Netherlands. Other minor players included Russia, Denmark, Sweden, and Germany. The entire continents of North and South America were colonized, including all the Caribbean islands. Most countries on the American mainland became independent by the mid 1800s, but most island nations did not become independent until the mid 1900s.

2nd Age of Imperialism:

The main European countries who colonized Africa and Asia were Great Britain, France, Germany, and Russia Other minor players included Italy, Spain, Belgium, the Netherlands, and Portugal. Almost the entire continent of Africa was colonized and the majority of the Asian continent was either colonized or acted like satellite states. Most countries became independent in the mid 1900s.