Similar to free surfaces, the grain boundaries (GBs) in metals, semiconductors and insulators can contain flat (faceted) and curved (rough) portions. In the majority of cases, facets are parallel to the most densely packed planes of coincidence sites lattice formed by two lattices of abutting grains. Facets disappear with the increasing temperature (faceting-roughening transition) and the increasing angular distance from coincidence misorientation. The temperature of GB faceting-roughening transition T (R) decreases with the increasing inverse density of coincidence sites I pound. In case of fixed I pound, T (R) decreases with the decreasing density of coincidence sites in the GB plane. The intersection line (ridge) between facets or between facets and curved (rough) portions of surfaces can be of first order (two different tangents in the contact point) or of second order (common tangent, continuous transitions). The rough (curved) portions of GB can also form the first-order rough-to-rough ridges (with two tangents). GB facets control the transition from normal to abnormal grain growth and strongly influence the GB migration, diffusion, wetting, fracture and electrical conductivity.