Continuously variable transmission (CVT) mechanisms combine the functions of a K-H-V type differential gear unit and a V-belt type continuously variable unit (CVU). For the 24 different mechanisms, 12 of them are power circulation modes while the other 12 are power split modes. Some useful theoretical formulas related to speed ratio, power flow and efficiency were derived and analyzed. These mechanisms have many advantages: they decrease CVT size and weight, increase overall efficiency, extend speed ratio range, and generate geared neutral. Compound CVTs were developed by combining the power circulation mode and power split mode, which can offer backward motion, geared neutral, underdrive and overdrive.