Introduction  Tokamak is recognized as the most feasible program for fusion power source, however various physical and engineering technology problems should be overcome before being power source. Error field, as inevitable non-axisymmetric perturbation magnetic field, can induce locked mode and degrade plasma stored energy, and further degrade the fusion reaction rate, or even resulting in disruption and damaging first wall of the device, threatening the safety and economy of fusion reactors. Therefore, it has been considered to be one of the most concerned problems in tokamaks over 30 years.

  Method  To clarify the progress of error field investigation, we reviewed the history of error field investigation, summarized the research achievements over 40 years from the aspects of experiment, theoretical analysis and numerical simulation.

  Result  On the basis of error field progress, we list the most concerned and unresolved problems in error field investigation in the world.

  Conclusion  We expect that this paper will provide some guidance for further investigations on frontier problems of error field, and help to contribute our strength to the knowledge of magnetically confined fusion physics.