Weyl semimetals are extraordinary systems where exotic phenomena such as
Fermi arcs, pseudo-gauge fields and quantum anomalies arise from topological
band degeneracy in crystalline solids for electrons and metamaterials for
photons and phonons. On the other hand, higher-order topological insulators
unveil intriguing multidimensional topological physics beyond the conventional
bulk-edge correspondences. However, it is unclear whether higher-order topology
can emerge in Weyl semimetals. Here, we report the experimental discovery of
higher-order Weyl semimetals in its phononic analog which exhibit
topologically-protected boundary states in multiple dimensions. We create the
physical realization of the higher-order Weyl semimetal in a chiral phononic
crystal with uniaxial screw symmetry. Using near-field spectroscopies, we
observe the chiral Fermi arcs on the surfaces and a new type of hinge arc
states on the hinge boundaries. These topological boundary arc states link the
projections of Weyl points in different dimensions and directions, and hence
demonstrate higher-order multidimensional topological physics in Weyl
semimetals. Our study establishes the fundamental connection between
higher-order topology and Weyl physics in crystalline materials and unveils a
new horizon of higher-order topological semimetals where unprecedented
materials such as higher-order topological nodal-lines may emerge