This article presents recent advancements in the development of flexible piezoresistive strain sensors based on carbon nanotubes (CNTs)–polymer composites, with particular attention to their electromechanical properties. Various fabrication approaches and material preparation of CNTs–polymer composites with improved piezoresistive performance are introduced. Moreover, the article presents the working principle of the piezoresistive sensors in terms of the tunneling effect and disconnection-reconnection mechanism. The sensing performances of recently reported applications are studied. This work also reveals that the CNTs–polymer composites have great potential for flexible, skin-mountable, and wearable electronics applications. Finally, possible challenges for the future developments of CNTs–polymer composites are discussed.