Flexible electronics offer a wide-variety of applications such as flexible circuits, flexible displays, flexible solar cells, skin-like pressure sensors, and conformable RFID tags. Carbon nanotubes (CNTs) are a promising material for flexible electronics, both as the channel material in field-effect transistors (FETs) and as transparent electrodes, due to their high intrinsic carrier mobility, conductivity, and mechanical flexibility. In this feature article, we review the recent progress of CNTs in flexible electronics by describing both the processing and the applications of CNT-based flexible devices. To employ CNTs as the channel material in FETs, single-walled carbon nanotubes (SWNTs) are used. There are generally two methods of depositing SWNTs on flexible substrates-transferring CVD-grown SWNTs or solution-depositing SWNTs. Since CVD-grown SWNTs can be highly aligned, they often outperform solution-processed SWNT films that are typically in the form of random network. However, solution-based SWNTs can be printed at a large-scale and at low-cost, rendering them more appropriate for manufacturing. In either case, the removal of metallic SWNTs in an effective and a scalable manner is critical, which must still be developed and optimized. Nevertheless, promising results demonstrating SWNT-based flexible circuits, displays, RF-devices, and biochemical sensors have been reported by various research groups, proving insight into the exciting possibilities of SWNT-based FETs. In using carbon nanotubes as transparent electrodes (TEs), two main strategies have been implemented to fabricate highly conductive, transparent, and mechanically compliant films-superaligned films of CNTs drawn from vertically grown CNT forests using the "dry-drawing" technique and the deposition or embedding of CNTs onto flexible or stretchable substrates. The main challenge for CNT based TEs is to fabricate films that are both highly conductive and transparent. These CNT based TEs have been used in stretchable and flexible pressure, strain, and chemical and biological sensors. In addition, they have also been used as the anode and cathode in flexible light emitting diodes, solar cells, and supercapacitors. In summary, there are a number of challenges yet to overcome to optimize the processing and performance of CNT-based flexible electronics; nonetheless, CNTs remain a highly suitable candidate for various flexible electronic applications in the near future.