Hydrogen sensing represents an important technique in a wide range of applications for 'hydrogen economy' such as industrial processing, fuel cells, hydrogen storage and separation, etc. Conventional hydrogen sensors are fabricated, in general, on rigid substrates (e.g., glass, quartz, silicon wafers) by using continuous as well as discontinuous palladium films (or wires) with lateral dimensions on the nanometer scales. The rigidity (and/or fragility) of these devices somehow limits their application in systems with curvilinear surfaces that require conformal lamination and mechanical shock-resistance. In contrast, hydrogen sensing devices fabricated on flexible polymeric substrates can find applications complementary to that of the conventional sensors on rigid substrates. We have recently found that nanoclusters of palladium deposited on the support of networks of single-walled carbon nanotubes significantly change the transport property of carbon nanotubes when the composites are exposed to hydrogen. Printing thin films of the Pd/nanotube composites on poly(ethylene terephthalate) (PET) sheets generates light-weight, shock-resistive, flexible hydrogen sensors. The as-fabricated devices have excellent performance which is comparable (even higher) to the conventional sensors. For example, these sensors can detect hydrogen with concentration as low as 30 ppm in air. The response time is as short as 7.5 second when the devices are exposed to 0.1% hydrogen in air at room temperature.