by @Chris
From Columbus's first landfall to the surrender of the last Spanish garrisons at Callao and Chiloé: how Spain and Portugal conquered Middle and South America, and how their empires broke up into new states. The Aztec and Inca empires fall within fifteen years of each other; silver towns, missions and cattle ranches then push the frontier outward for three centuries, while the Dutch, French and English take islands and coasts. Bourbon Spain splits Peru into three viceroyalties; after 1808 juntas, royalist reconquests and the campaigns of Bolívar and San Martín redraw the map almost every year. The map shows effective control, not claims: land that was conquered, settled, garrisoned or missionised. Unconquered regions (Amazonia, the Chaco, Patagonia, the Mapuche lands, the far north of New Spain) stay empty, and the Tordesillas line shows what the treaties said instead. Simplifications: borders follow modern provinces, with disks around frontier towns, forts and missions and bands along coasts and rivers; small islands are drawn as disks; Venezuela counts under New Spain until 1717 (it answered to the Audiencia of Santo Domingo); royalist-held land keeps its viceroyalty colour during the wars of independence, and patriot-held land takes the colour of the later state. British North America and the United States are context only. Sources: Wikipedia (English, Spanish, Portuguese) on the conquests, the viceroyalties, Dutch Brazil, the treaties of Tordesillas, Madrid and San Ildefonso, and the wars of independence. Aztec, Maya and Inca outlines: Cliopatria (Seshat Global History Databank, CC BY 4.0); borders: Natural Earth.
Mapuche lands (Araucanía) · Other native states (Taíno, Purépecha, Tlaxcala, Muisca, Tairona …) · Maya states (Yucatán, highlands; Itza to 1697) · Aztec Triple Alliance · Inca Empire (Vilcabamba to 1572) · Spain: Crown lands outside a viceroyalty (to 1535/42; Cuba, Puerto Rico from 1821) · Spain: Viceroyalty of New Spain (1535–1821) · Spain: Viceroyalty of Peru (1542–1824) · Spain: Viceroyalty of New Granada (1717–23, 1739–1822) · Spain: Viceroyalty of the Río de la Plata (1776–1814) · Portuguese Brazil · Empire of Brazil (1822) · Dutch (West India Company, Suriname, Curaçao) · France · England → Great Britain · United States · Haiti (1804) · Mexico (insurgents 1810–21; Empire 1821, Republic 1823) · United Provinces of Central America (1821/23) · Venezuelan and New Granadan patriots → Colombia (1819) · Peru (patriots; republic 1821) · Bolivia (1825) · Chile (1810–14, 1817) · United Provinces of the Río de la Plata (1810) · Paraguay (1811) · Line of Tordesillas (1494): Portugal east, Castile west