The attractive structural and mechanical properties of cellulose substrates (paper, cloth, and thread), including passive fluid transport, biocompatibility, durability, and flexibility, have attracted researchers in the past few decades to explore them as alternative microfluidic platforms. The incorporation of electrochemical (EC) sensing broadened their use for applications such as clinical diagnosis, pharmaceutical chemical analyses, food quality, and environmental monitoring. This article provides a review on the microfluidic devices constructed on paper, cloth, and thread substrates. It begins with an overview on paper-based microfluidic devices, followed by an in-depth review on the various applications of EC detection incorporated on paper-based microfluidic devices reported to date. The review on paper-based microfluidic devices attempts to convey a few perspective directions that cloth- and thread-based microfluidic devices may take in its development. Finally, the research efforts on the development and evaluation, as well as current limitations of cloth- and thread-based microfluidic devices are discussed. Microfluidic devices constructed on paper, cloth, and thread substrates are still at an early development stage (prototype) requiring several improvements in terms of fabrication, analytical techniques, and performance to become mature platforms that can be adapted and commercialized as real world products. However, they hold a promising potential as wearable devices.