A brief review about carbon nanotube is presented at first, followed by nnnnnna brief review of ternary logic and then finally some of the ternary logic circuit built with carbon nanotube field effect transistor (CNTFET) are discussed. Recent progress in ternary logic circuit proposed by using CNTFET as basic building block is discussed in this paper. Complementary CNTFET designs are used to build ternary logic circuits just like Complementary CMOS designs. MVL has gained its popularity as binary logic circuits are reaching its limitations. Different CNTFET Ternary logic circuits like half adder (HA), full adder (FA) and multiplier circuits are studied and a brief review is presented in this paper about how different designs and different methodologies are proposed to achieve high performance, low power consuming and also with less delay.