Topological metals (TMs) are a kind of special metallic materials,which feature nontrivial band crossings near the Fermi energy,giving rise to peculiar quasiparticle excitations.TMs can be classified based on the characteristics of these band crossings.For example,according to the dimensionality of the crossing,TMs can be classified into nodal-point,nodal-line,and nodal-surface metals.Another important property is the type of dispersion.According to degree of the tilt of the local dispersion around the crossing,we have type-Ⅰ and type-Ⅱ dispersions.This leads to significant distinctions in the physical properties of the materials,owing to their contrasting Fermi surface topologies.In this article,we briefly review the recent advances in this research direction,focusing on the concepts,the physical properties,and the material realizations of the type-Ⅱ nodal-point and nodal-line TMs.