State of the art in the determination of the fine structure constant and the ratio $h/m_\mathrm{u}$

The fine structure constant $\alpha$ and the ratio $h/m_{\mathrm{u}}$ between the Planck constant and the unified atomic mass are keystone constants for the determination of other fundamental physical constants, especially the ones involved in the framework of the future International System of units. This paper presents how these two constants, which can be deduced from one another, are measured. We will present in detail the measurement of $h/m_\mathrm{Rb}$ performed by atomic interferometry at the Laboratoire Kastler Brossel in Paris. This type of measurement also allows a test of the standard model to be carried out with unparalleled accuracy.