Magnetic fields play a key role in driving a broad range of dynamic phenomena in the atmospheres of the Sun and other stars. Routine and accurate measurements of the magnetic fields at all the atmospheric layers are of critical importance to understand these magnetic activities, but in the solar and stellar coronae such a measurement is still a challenge due to the weak field strength and the high temperature. Recently, a magnetic-field-induced transition (MIT) of Fe x at 257.26 Å has been proposed for the magnetic field measurements in the solar and stellar coronae. In this review, we present an overview of recent progresses in the application of this method in astrophysics. We start by introducing the theory underlying the MIT method and reviewing the existing atomic data critical for the spectral modeling of Fe x lines. We also discuss the laboratory measurements that verify the potential capability of the MIT technique as a probe for diagnosing the plasma magnetic fields. We then continue by investigating the suitability and accuracy of solar and stellar coronal magnetic field measurements based on the MIT method through forward modeling. Furthermore, we discuss the application of the MIT method to the existing spectroscopic observations obtained by the Extreme-ultraviolet Imaging Spectrometer onboard Hinode. This novel technique provides a possible way for routine measurements of the magnetic fields in the solar and stellar coronae, but still requires further efforts to improve its accuracy. Finally, the challenges and prospects for future research on this topic are discussed.