Spain came to dominate the majority of Latin America as a result of its colonization efforts that began in the late 15th century. Hernan Cortes conquered the Aztec Empire in 1521, and the Spanish Empire subsequently established its rule over much of Central and South America.
As for Portugal, it primarily focused its colonization efforts on the eastern coast of South America, specifically Brazil. Pedro Alvares Cabral claimed the land for Portugal in 1500, and Brazil remained under Portuguese rule until the 19th century.