Disclosed herein are power transmissions having one or more operational modes, for example, a continuously variable transmission (CVT) mode, an infinitely variable transmission (IVT) mode, and an IVT/CVT mode, that can be selected for by engaging different clutches and brakes. Disclosed herein are power transmissions comprising a power input shaft, one or more planetary gear sets, a variator (such as a CVT), and one or more clutches and brakes. In some embodiments, a first brake selects an IVT mode, a second brake selects a CVT mode, and a third brake selects an IVT/CVT mode.