In this book chapter, a brief introduction is provided to CNTs, its material science, modelling, simulation and circuit application. CNTs are explored from electronic properties as the nature of conduction, i.e., metallic and semiconducting. Chirality is explained, which is responsible for basic parameters calculations like diameter and bandgap. Considering the excellent characteristics of CNT, how they are used as channel materials in MOSFETs is discussed along with the type of CNTFET. The physics behind the working of CNTFET is explained for every type along with advantages and disadvantages of device type. Since CNTFETs have many challenges for future devices, the most important challenge of doping is discussed along with the novel solution, i.e., electrostatic doping. The concept of electrostatic doping is explained with the help of a band diagram as how the biases at polarity gates are used to shift the bands the same as in conventional doping. The characteristics of an ED device are compared with a conventional doped device in order to get better understanding and advantage of the device. The only available benchmark simulation tool for CNTFETs is discussed along with the model used in calculations of drain current. Also the different types of CNTFETs are simulated in this tool, and the characteristics are shown. Apart from conventional CNTFET, ED CNTFET is also simulated in the tool in order to check the results. Along with numerical tool for simulation, the various approaches that can be used to model the device are discussed. The equations are explained with device physics for both conventional CNTFET and ED CNTFET. Lastly, the circuit applications are discussed ranging from analog to digital applications.