Impossible Indians is a study of 20th-century U.S. Latina/o and Latin American theatre and performance artists whose works of art are inspired by the 15thand 16th-century Conquest of the Americas. The "decolonial turn" in Latin American and U.S. Latina/o Studies urges scholars to theorize post/colonialism from the birth of modernity/coloniality in the Americas during the early colonial period. Few studies, however, have theorized the place of performance in the consolidation of modernity/coloniality. While the formal colonization of non-indigenous people in the Americas has a beginning (the Conquest) and a presumed end (colonial independence), colonialism is also a process that haunts their postcolonial imaginary in what José Rabasa has called "a ghost-like continuity" that staged and restaged for centuries. My dissertation theorizes this tragic framework by studying the ways in which dramatic artists consistently turn to indigenous colonial and pre-Columbian pasts as a manner of imagining their own racial present bound to the history of colonialism in the New World. I argue that playwrights like Rodolfo Usigli, Cherríe Moraga, Sergio Magaña, William Shakespeare, Aimé Césaire, and Migdalia Cruz, and performance artists like Coco Fusco, Guillermo Gómez-Peña, Antonin Artaud, and Nao Bustamante, stage a vision of the their modern world that questions the linear temporality attributed to historical formations of race. In creating their racial presents vis-à-vis ideologies of indigeneity that are always-already originating outside of modern time, the subjects of my dissertation stage colonialism as an unfinished process by strategically returning to scenarios of conquest. My argument is two fold: I trace the employment of performative and archival knowledge as ethnographic tools to invent the indigenous racial subject of the Americas from a colonial and colonizing standpoint; and I analyze theatre and performance art that have crated decolonial ideals of indigeneity and indigenous people in order to reproduce and discard racial ideologies transferred from the colony to the postcolonial. I insist that this mode of cultural production creates a cultural politics of conquest that poses a radical challenge to linear conceptions of both race and time.