Different solar atmospheric layers are connected by the magnetic field of the Sun, which is the primary source for various types of solar activity. The magnetic activity of the Sun has a significant impact on the solar-terrestrial environment and human life. Understanding the phenomena occurring in the solar atmosphere relies on a thorough understanding of the solar magnetic field. However, up to now, only the magnetic field at the photospheric level can be measured with precision on a daily basis. No routine measurements have been carried out for the magnetic field in the upper layers of the solar atmosphere, particularly the solar corona. The lack of coronal magnetic field measurements has limited our investigation of many important topics in solar physics research including the driving mechanism of solar eruptions and the heating process of corona. In the past several decades, a number of techniques that may be useful for coronal magnetic field diagnostics have been developed, such as the techniques based on infrared spectro-polarimetry of coronal lines, the diagnosis utilizing coronal radio observations, magneto-seismology using observations of coronal magnetohydrodynamics waves and the measurements based on the magnetic-field-induced transition of coronal extreme ultraviolet spectral lines. Meanwhile, a few attempts have been made to measure the coronal magnetic field based on these techniques. This review summarizes the physical principles and important progress of coronal magnetic field measurements, and discuss future perspectives on related research.