Aging epithelia are colonized by somatic mutations, which are subjected to selection influenced by intrinsic and extrinsic factors. The lack of suitable culture systems has slowed the study of this and other long-term biological processes. Here, we describe epithelioids, a facile, cost-effective method of culturing multiple mouse and human epithelia. Esophageal epithelioids self-maintain without passaging for at least 1 year, maintaining a three-dimensional structure with proliferative basal cells that differentiate into suprabasal cells, which eventually shed and retain genomic stability. Live imaging over 5 months showed that epithelioids replicate in vivo cell dynamics. Epithelioids support genetic manipulation and enable the study of mutant cell competition and selection in three-dimensional epithelia, and show how anti-cancer treatments modulate competition between transformed and wild-type cells. Finally, a targeted CRISPR–Cas9 screen shows that epithelioids recapitulate mutant gene selection in aging human esophagus and identifies additional drivers of clonal expansion, resolving the genetic networks underpinning competitive fitness.