Variable-ratio transmission of mechanical shaft power is one of the essential capabilities that render mechanical systems a required dynamibility. Mechanical continuously variable transmissions (CVTs) are broadly classified into rolling types and gripping types. The former are presented with emphasis on the smallness of the curvature mismatch of the rolling surfaces as an essential feature for achieving higher power density, and to show how the rolling sphere–torus types could not measure-up to those “surviving designs.” One type that has been famous for its dynamibility in the automotive driveline is shown why it has been taken out of production. The latter, gripping types (of the higher power density) are scrutinized to reveal the “obscure” problems with one design and the superiority of another. Mechanical infinitely variable transmissions (IVTs) are also dealt with to reveal their inherent problems.