We explain the construction of the curved Gerstenhaber calculus associated with a deformation problem of Gerstenhaber calculi, and thus associated with a logarithmic deformation problem. This curved Gerstenhaber calculus is called the “characteristic Gerstenhaber calculus.” We prove that deformations correspond with gauge equivalence classes of solutions of the extended Maurer–Cartan equation. At the beginning of the chapter, we review the Thom–Whitney resolution, which is an important tool in the construction of the characteristic Gerstenhaber calculus.