  A critical point of the energy dispersion is the momentum where electron
velocity vanishes. At the corresponding energy, the density of states (DOS)
exhibits non-analyticity such as divergence. Critical points can be first
classified as ordinary and high-order ones, and the ordinary critical points
have been studied thoroughly by L\'eon van Hove. In this work, we describe and
classify high-order critical points based on topology, scaling and symmetry,
which are beyond L\'eon van Hove's framework. We show that high-order critical
points can have power-law divergent DOS with particle-hole asymmetry, and can
be realized at generic or symmetric momenta by tuning a few parameters such as
twist angle, strain, pressure and/or external fields.
