Sapa Inca in the context of "Huayna Capac"

The Incas were most notable for establishing the Inca Empire which was centered in modern-day Peru and Chile. It was about 4,000 kilometres (2,500 mi) from the northern to southern tip. The Inca Empire lasted from 1438 to 1533. It was the largest Empire in America throughout the Pre-Columbian era. The Inca state was originally founded by Manco Cápac in the early 1200s, and is known as the Kingdom of Cuzco. Under subsequent rulers, through strategic alliances and conquests, it expanded beyond Cusco and into the Sacred Valley. Their territory then rapidly grew under the 9th Sapa Inca (emperor), Pachacuti and his descendents.

Over the course of the Inca Empire, the Inca used conquest and peaceful assimilation to incorporate the territory of modern-day Peru, followed by a large portion of western South America, into their empire, centered on the Andean mountain range. However, shortly after the Inca Civil War, the last Sapa Inca of the Inca Empire, Atahualpa, was captured and killed on the orders of the conquistador Francisco Pizarro, marking the beginning of Spanish rule. The remnants of the empire retreated to the remote jungles of Vilcabamba and established the small Neo-Inca State, which was conquered by the Spanish in 1572.

The Spanish conquest of the Inca Empire, also known as the Conquest of Peru, was one of the most important campaigns in the Spanish colonization of the Americas. After years of preliminary exploration and military skirmishes, 168 Spanish soldiers under conquistador Francisco Pizarro, along with his brothers in arms and their indigenous allies, captured the last Sapa Inca, Atahualpa, at the Battle of Cajamarca in 1532. It was the first step in a long campaign that took decades of fighting but ended in Spanish victory in 1572 and colonization of the region as the Viceroyalty of Peru. The conquest of the Inca Empire (called "Tahuantinsuyu" or "Tawantinsuyu" in Quechua, meaning "Realm of the Four Parts"), led to spin-off campaigns into present-day Chile and Colombia, as well as expeditions to the Amazon Basin and surrounding rainforest.

When the Spanish arrived at the borders of the Inca Empire in 1528, it spanned a considerable area and was by far the largest of the four grand pre-Columbian civilizations. Extending southward from the Ancomayo, which is now known as the Patía River, in southern present-day Colombia to the Maule River in what would later be known as Chile, and eastward from the Pacific Ocean to the edge of the Amazonian jungles, it covered some of the most mountainous terrains on Earth. In less than a century, the Inca had expanded their empire from about 400,000 km (150,000 sq mi) in 1448 to 1,800,000 km (690,000 sq mi) in 1528, just before the arrival of the Spanish. This vast area of land varied greatly in culture and climate. Because of the diverse cultures and geography, the Inca allowed many areas of the empire to be governed under the control of local leaders, who were watched and monitored by Inca officials. Under the administrative mechanisms established by the Inca, all parts of the empire answered to, and were ultimately under the direct control of, the Inca Emperor. Scholars estimate that the population of the Inca Empire was between 12 and 16 million.

The Inca society was the society of the Inca civilization in Peru. The Inca Empire, which lasted from 1438 to 1533 A.D., represented the height of this civilization. The Inca state was known as the Kingdom of Cusco before 1438. Over the course of the empire, the rulers used conquest and peaceful assimilation to incorporate a large portion of western South America, centered on the Andes mountain ranges. The empire proved relatively short-lived however: by 1533, Atahualpa, the last Sapa Inca (emperor) of the Inca Empire, was killed on the orders of the conquistador Francisco Pizarro, marking the beginning of Spanish rule. The last Inca stronghold, the Neo-Inca State in Vilcabamba, was conquered by the Spanish in 1572.

Topa Inca Yupanqui or Túpac Inca Yupanqui (Cusco Quechua: Thupa Inka Yupanki, pronounced [ˈtʰupa ˈiŋka juˈpaŋki]), also Topa Inga Yupangui, erroneously translated as "noble Inca accountant" (before 1471 – 1493) was the tenth Sapa Inca (1471–1493) of the Inca Empire, fifth of the Hanan dynasty. His father was Pachacuti, and his son was Huayna Capac. Topa Inca belonged to the Qhapaq Panaca (one of the clans of Inca nobles). His quya (principal wife) was his older sister, Mama Ocllo.

Qullasuyu (Quechua and Aymara spelling, listen; Collasuyu, Kholla Suyu; Spanish: Collasuyo) was the southeastern provincial region of the Inca Empire. Qullasuyu is the region of the Qulla and related specifically to the native Qulla Quechuas who primarily resided in areas such as Cochabamba and Potosí. Most Aymara territories which are now largely incorporated into the modern South American states of northern Chile, Peru, Bolivia and the Argentine northwest were annexed during the reign of Sapa Inca Huayna Cápac in the sixteenth century.

Recently, there have been movements to form a "Greater Qullasuyu" (or Qullana Suyu Marka) which would incorporate a territory similar to the former Tawantinsuyu in extent. This ideal has been proposed by the office of the Apu Mallku and the parliament of the Qullana. Qullasuyu was the largest of the four suyu (or "quarters", the largest divisions of the Inca empire) in terms of area. This suyu encompassed the Bolivian Altiplano and much of the southern Andes, running down into northwest Argentina and as far south as the Maule river near modern Santiago, Chile. Along with Kuntisuyu, it was part of the Hurin Suyukuna or "Lower Quarters" of the empire.

Pachacuti Inca Yupanqui, also called Pachacútec (Quechua: Pachakutiy Inka Yupanki, pronounced [ˈpatʃa ˈkuti ˈiŋka juˈpaŋki]), was the ninth Sapa Inca of the Chiefdom of Cusco, which he transformed into the Inca Empire (Tawantinsuyu). Most archaeologists now believe that the famous Inca site of Machu Picchu was built as an estate for Pachacuti.

In Quechua, the cosmogonical concept of pachakutiy means "the turn of the world" and yupanki could mean "honorable lord". During his reign, Cusco grew from a hamlet into an empire that could compete with, and eventually overtake, the Chimú empire on the northern coast. He began an era of conquest that, within three generations, expanded the Inca dominion from the valley of Cusco to a sizeable part of western South America. According to the Inca chronicler Garcilaso de la Vega, Pachacuti created the Inti Raymi to celebrate the new year in the Andes of the southern hemisphere. Pachacuti is often linked to the origin and expansion of the cult of Inti.

Atahualpa (/ˌɑːtəˈwɑːlpə/ ), also Atawallpa or Ataw Wallpa (Classical Quechua: Ataw Wallpa, pronounced [ˈataw ˈwaʎpa]) (c. 1502 – 26 July 1533), whose regnal name was Caccha Pachacuti Inca Yupanqui Inca (from the caccha idol and to honour the emperor Pachacuti), was the last effective Inca emperor, reigning from April 1532 until his capture and execution in July of the following year, as part of the Spanish conquest of the Inca Empire.

Manco Inca Yupanqui (c. 1515 – 1544) was the founder and first Sapa Inca of the independent Neo-Inca State in Vilcabamba, although he was originally a puppet Inca Emperor installed by the Spaniards. He was also known as Manco II and Manco Cápac II. He was one of the sons of Huayna Cápac and a younger brother of Huáscar.