Fully textile smart wearables will be the result of the complete integration and miniaturization of electronics and textile materials. Off-body communications are key for connecting smart wearables with external devices, even for wireless power transfer or energy harvesting. They need to fulfill specific electromagnetic (EM) (impedance bandwidth (BW), gain, efficiency, and front to back radiation (FTBR)) and mechanical (bending, crumpling, compression, washing and ironing) requirements so that the smart wearable device provides the required performance. Therefore, textile and flexible antennas require a proper trade-off between materials, antenna topologies, construction techniques, and EM and mechanical performances. This review shows the latest research works for textile and flexible planar, fully grounded antennas for off-body communications, providing a novel design guide that relates key antenna performance parameters versus topologies, feeding techniques, conductive and dielectric textile materials, as well as the behavior under diverse measurement conditions.