Development of electrodeless radiofrequency plasma thrusters, e.g., a helicon thruster, has been one the of challenging topics for future high-power and longlived electric propulsion systems. The concept simply has a radiofrequency plasma production/heating source and a magnetic nozzle, while it seems to include many aspects of physics and engineering issues. The plasma produced inside the source is transported along the magnetic field lines and expands in the magnetic nozzle, where the plasma is spontaneously accelerated into the axial direction along the magnetic nozzle, yielding a generation of the thrust force. Hence, the plasma transport and spontaneous acceleration phenomena in the magnetic nozzle are key issues to improve the performance of the thrusters. Since the thrust is equal in magnitude and opposite in direction to momentum flux exhausted from the system, the direct measurement of the thrust can reveal not only the thruster performance but also fundamental physical quantity of plasma momentum flux. Here studies on fundamental physics relating to the thruster development and the technology for the compact and efficient system are reviewed; the current status of the thruster performance is shown. Finally, a recently proposed future new application of the thruster is also discussed.