Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.