Hernán Cortés was dazzled by the splendor of the Aztec capital Tenochtitlán, which is not surprising because the Mexica empire, at that time, was at the height of its power. Almost at the same time, the conquistadors discovered the last bastions of postclassical Mayan civilization in the Yucatán. This course of history explains why it is mainly the Aztec and Maya civilizations that are known to us through pre-Columbian texts. In the case of the Maya, only four pre-Columbian codices and some sacred writings (Popol Vuh, Chilam Balam, ...) have been preserved. More Aztec documents survive. This is the case for a certain number of codices prior to the Spanish conquest. The importance of astronomy in the ancient civilizations of Mesoamerica should not be underestimated. Observing the Sun was vital but it was also the case for the moon, the Pleiades and the brightest planets, Venus being by far the most observed one. The need for precise astronomical observations arose with developments in agriculture, due to the fact that certain cyclical changes observed in the sky coincide with seasonal modifications in the natural environment. The measurement of time also attracted very much the attention of Mesoamerican peoples. These different civilizations, notably the Aztecs and the Maya, used a civil calendar and another sacred one, the intertwining of both being considered with care.