An overview of the natural mode method is presented, as applied in the linear and geometrically nonlinear analysis of multilayered composite plates and shells of arbitrary geometry. The method is particularly suitable for the finite element analysis of thin and moderately thick composite shell structures using simple 3-node triangular plate and shallow shell elements which are based on the definition of total strain, as well as physical decomposition principles, and involve only exact integrations. The triangular elements comprise 12 degrees of freedom on the natural coordinate. Numerical examples have shown that they address a well-balanced trade-off between accuracy and economy; as such they are intended for the analysis of large and complex composite shell structures and for use in interdisciplinary topics such as efficient sensitivity analysis and design optimization where complexity and economy must be considered in the computations. A brief history of the evolution of the natural mode technique is also given. Areas of application include static, vibration, buckling, postbuckling, and nonlinear dynamic and chaotic response topics under both load and temperature. This review article includes 36 references.