Stretchable electronics has evolved rapidly in the past decade because of its promising applications, as electronic devices undergo large mechanical deformation (e.g., bending, folding, twisting, and stretching). Stretchable conductors are particularly crucial for the realization of stretchable electronic devices. Therefore, tremendous efforts have been dedicated toward developing stretchable conductors, with a focus on conductive material/polymer composites. This review summarizes the recent progress in stretchable conductors and related stretchable devices based on carbon nanotubes (CNTs), which was enabled by their outstanding electrical and mechanical properties. Various strategies for developing highly stretchable conductors that can deform into nonplanar shapes without significant degradation in their electronic performance are described in terms of preparation processes. Finally, challenges and perspectives for further advances in CNT-based stretchable conductors are discussed.