The supercapacitors are advanced electrochemical energy storage devices having characteristics such as high storage capacity, rapid delivery of charge, and long cycle life. Polypyrrole (PPy) – an electronically conducting polymer, and carbon nanotubes (CNT) with high surface area and exceptional electrical and mechanical properties are among the most frequently studied advanced electrode materials for supercapacitors. The asymmetric supercapacitors composed of PPy/CNT composite electrodes offer complementary benefits to improve the specific capacitance, energy density, and stability. This article presents an overview of the recent technological advances in PPy/CNT composite supercapacitors and their limitations. Various strategies for synthesis and fabrication of PPy/CNT composites are discussed along with the factors that influence their ultimate electrochemical performance. The drawbacks and challenges of modern PPy/CNT composite supercapacitors are also reviewed, and potential areas of concern are identified for future research and development.