Classical (linear) elasticity is a very old subject, and its planar/2D cases (plane stress and plane strain) equally so. However, the possibility of having the same stress field in 2D materials whose (generally spatially inhomogeneous) elastic moduli are different but satisfy certain relations is a relatively new result. This reduced parameter dependence has consequences for the effective moduli of composite materials, including the special case of a plate perforated by holes (especially up to the percolation point), and lends itself to extensions, such as the presence of body force fields or thermal stresses. These issues, including a short section on poroelasticity, are reviewed in this chapter.