An overview of the analytical solutions for the elastic fields of nanoinclusions in composite solids is given. Special attention is paid to the case of nanocomposites. Besides, a description of the most popular analytical procedures for the calculations of the elastic fields of inclusions in nanocomposites is provided. These procedures include the Green function method, the method of surface dislocation loops, integration of the equations of equilibrium, and the method of infinitesimal inclusions. Also, the solutions for the elastic fields of nanoinclusions, derived within linear elasticity, are discussed and compared with those obtained using atomistic simulations. It is shown that the linear elasticity approach is valid down to extremely small dimensions of nanoinclusions.