As an exotic topological state, the Weyl semimetal (WSM) was discovered in realistic materials (e.g. TaAs and MoTe2) recently, by observing unique Fermi arcs on the surface spectroscopy and revealing the chiral anomaly effect in the bulk magneto-transport. In this talk, I will focus on the linear and nonlinear responses for these WSM materials as a manifestation of the bulk band structure topology. In the linear response regime, WSMs show an intrinsic anomalous Hall effect or spin Hall effect of WSMs. The second-order response, caused by the huge Berry curvature near Weyl points, can lead to very strong nonlinear optical effects such as photocurrents and the second harmonic generation.