He is primarily known for his work Historia general del Piru (written c. 1580-1616), which is considered the earliest illustrated history of Peru.
He later traveled throughout the Viceroyalty of Peru as a missionary, serving in the proximities of Lake Titicaca and Cuzco, where he came to know some features of the inhabitants of the former Inca Empire well.
The following year, while living in Madrid, Murúa received the necessary authorizations from both his Order and the king to publish his chronicle, entitled Historia general del Piru.
In his Historia, Murúa wrote of the presence of a number of mythological creatures in South America, such as Amazons and giants, which gave rise to the names of many geographical landmarks of the continent.
This first version of the chronicle was compiled in Peru by Murúa with the assistance of local scribes and Indigenous artists (one of whom was Felipe Guaman Poma de Ayala).
In the 1950s, the manuscript was bought by a rare bookseller in San Francisco, California and resold to the late John Galvin (d. 1996), a European aristocrat and private collector.
It was later sold at auction to a collector in Cologne, Germany, changing hands once more before its "rediscovery" by Manuel Ballesteros Gaibrois in the early 1950s.
The most striking feature of the chronicle is its numerous illustrations, which include portraits of Inca nobility and depictions of traditional ceremonies.
There is strong evidence that the chroniclers Guamán Poma and Martín de Murúa met and there was a close collaboration between them that later ended in rupture.
The project's principal scholars included Juan de Ossio, Thomas Cummins, and Barbara Anderson, with collaboration by Rolena Adorno and Ivan Boserup.
Guamán Poma notably attacks Murúa in his Corónica, even depicting the friar striking and kicking an indigenous woman seated at a loom.
Although the evidence suggests that they worked independently after 1600, the efforts of Murúa and Guamán Poma can never be separated, and their talents, individually and together, produced three distinctive testimonies to the interaction between missionary author and indigenous artist-cum-author in early colonial Peru.