Abstract: Black hole X-ray binary (BHXRB) is a binary system consisting of a central compact black hole and its companion star. Its outburst phase is always accompanied by multi-wavelength emission. With the development of the multi-messenger astronomy, a general picture of the physical processes and spectral energy distribution (SED) behind the multi-wavelength radiation has been formed. The accretion disk and corona around the black hole dominate the X-ray emission; black hole X-ray binaries are always accompanied by jets, and the jets are the main source of radio emission; the physical process that dominates the optical/near-infrared emission is more complicated. It is generally believed that there are three physical processes involved, including X-ray reprocessing, viscous thermal radiation from the outer accretion disc, and jet emission. Many researches indicate that there is often a clear power-law correlation between the flux of the multi-wavelength emissions. This implies a correlation between the physical processes behind the multi-wavelength emissions. However, the specific physical processes underlying the association between the jet and the accretion disc remain unclear. It has been suggested that the weak external magnetic field in the BHXRB can be radially dragged inwards by the accretion disc to form a strong magnetic field near the black hole. This process results in a significant amplification of the magnetic field in the accretion flow. And it is a prerequisite for theoretical studies of the BZ (Blandford-Znajek) model and the BP (Blandford-Znajek) model for jet launching and acceleration. Also, the strong magnetic fields can change the structure of the internal accretion flow, possibly forming the magnetically arrested accretion disks (MADs) in regions close to the black hole. Using the broad band X-ray observations from Insight-HXMT (Insight Hard X-ray Modulation Telescope), we are able to glimpse the high-energy radiation processes occurring in such densely compact regions. The transfer of magnetic fields in BHXRBs may provide insights into, or partially explain, the coupling between the accretion disk and the jet. We will review the researches on BHXRB accretion magnetic field advection and jets over the decades, and introduce the recent research on black hole accretion and magnetic field advection.