Abstract: This talk is devoted to investigating the heat trace asymptotic expansion associated with the magnetic Steklov problem on a compact Riemannian manifold with boundary. By computing the full symbol of the magnetic Dirichlet-to-Neumann map, we establish an effective procedure, by which we can calculate all the coefficients of the asymptotic expansion. In particular, we explicitly give the first four coefficients. They are spectral invariants, which provide precise information concerning the volume and curvatures of the boundary and some physical quantities.