The line-operated vacuum tube receiver was invented in 1925 by Edward S. Rogers, Sr. The unit operated with 5 Rogers AC vacuum tubes and the Rogers Battery-Eliminator Power Unit (power supply). This unit was later marketed for $120  as "Type 120". He established the Toronto station CFRB (an abbreviation of Canadas First Rogers Batteryless') to promote sales of the product. Batteryless radios were not introduced into the United States until May 1926 and then into Europe in 1927.
Crystal radio receivers are a very simple kind of batteryless radio receiver. They do not need a battery or power source, except for the power that they receive from radio waves using their long outdoor wire antenna.  Sharp Electronics first electrical product was a batteryless crystal radio introduced in 1925.  It was Japans first -- and sold extremely well.
Thermoelectricity was widely used in the remote parts of the Soviet Union from the 1920s to power radios.  The equipment comprised some bi-metal rods (thermocouples), one end of which could be inserted into the fireplace to get hot with the other end left out in the cold.
After the Second World War, kerosene radios were made in Moscow for use in rural areas. These all-wave radios were powered by the kerosene lamp hanging above them. A group of thermocouples was heated internally to  by the flame. Fins cooled the outside to about . The temperature differential generated enough current to operate the low-drain receiver.
Foot-operated radio or pedal radio was once used in Australia. Other ways of achieving the same function are clockwork radio, hand crank radio and solar radio, especially for the Royal Flying Doctor Service and School of the Air.   
As part of an energy harvesting electronics system, some batteryless radios render electricity to storage by means of storage capacitors. In this batteryless type of radio, the storage capacitors cache the electricity as static on layers of dielectric instead of chemical changes, providing energy like batteries do but batteryless.  This can be quite effective.  Storage capacitors recharge millions of times, they are relatively cheap, somewhat insensitive to temperature, and they never need replacing -- which is why they are usually soldered on.  As part of an energy autarkic or energy harvesting batteryless radio, therefore, storage capacitors are an integral part, storing electricity like battery does for lean energy periods, but in a batteryless way which is more sustainable.  About 15 billion batteries are consumed every year worldwide.