Compared with traditional conductive fillers, carbon nanotubes (CNTs) have unique advantages, i.e., excellent mechanical properties, high electrical conductivity and thermal stability. Nanocomposites as piezoresistive films provide an interesting approach for the realization of large area strain sensors with high sensitivity and low manufacturing costs. A polymer-based nanocomposite with carbon nanomaterials as conductive filler can be deposited on a flexible substrate of choice and this leads to mechanically flexible layers. Such sensors allow the strain measurement for both integral measurement on a certain surface and local measurement at a certain position depending on the sensor geometry. Strain sensors based on carbon nanostructures can overcome several limitations of conventional strain sensors, e.g., sensitivity, adjustable measurement range and integral measurement on big surfaces. The novel technology allows realizing strain sensors which can be easily integrated even as buried layers in material systems. In this review paper, we discuss the dependence of strain sensitivity on different experimental parameters such as composition of the carbon nanomaterial/polymer layer, type of polymer, fabrication process and processing parameters. The insights about the relationship between film parameters and electromechanical properties can be used to improve the design and fabrication of CNT strain sensors.