Since their discoveries in 1990’s of last century and the beginning of this century, respectively, carbon nanotubes (CNTs) and graphenes have been extensively investigated. Investigations of the properties of CNTs and graphenes, either as single nanostructures or as components in nanoscale devices, such as molecular transporter or nanocomposites, have become one of the most active research directions in materials physics and chemistry and nanotechnology. The investigations include a wide range of studies on their electronic conductance properties, field emission properties, fracture and buckling properties, and thermal conductivity properties. The studies have exhibited extremely high strength and exceptional electronic and thermal properties of the nanostructures. The superior mechanical properties have generated a great motivation for mechanical engineers and scholars to explore potential applications of individual CNTs and graphenes, and nanoscale systems made from them. The efforts by the engineers and scholars have revealed wide potential applications of CNTs and graphenes in nanodevices in biological, medical, energy storage, sensor, and other engineering and medicine applications. The nanostructures have been found to hold substantial promises as nanosensors, oscillators, transistors, solar cells, molecular transporters, ultracapacitors, microbial detection, and diagnosis devices, etc. Extensive and comprehensive simulation and experimental studies on carbon nanotubes and graphenes will open a door for a wide range of their applications in engineering and medicine.