Drosophila imaginal discs, the precursors of the adult fly appendages, are an important system for studying mechanisms of cell determination. How the different imaginal discs acquire and maintain their appendage-specific determined states are problems that have been addressed using experimental embryology as well as genetic and molecular approaches. Here we discuss the concept of cell determination and describe what is known about how determination is established and maintained in imaginal disc cells. The phenomenon of imaginal disc transdetermination, originally discovered in the 1960s, has remained an intriguing problem for understanding imaginal disc cell determination. We review the topic of imaginal disc transdetermination and describe how recent results from molecular genetic approaches have provided new insights into imaginal disc transdetermination and determination. We also discuss how an understanding of imaginal disc transdetermination can aid our understanding of parallel phenomena in other organisms, including human metaplasias.