The article presents some modern developments in computational technology for the nonlinear thermostructural analysis of laminated composite plates and shells of arbitrary geometry. Following a review of the current state of the art, it particularly emphasizes on new finite element methodologies that can be applied to the study of complex laminated shells both thermally and structurally using the same topology constructed via simple simplex triangular elements based on respective first-order lamination theories. Very high temperatures are imposed on some examples in order to demonstrate the high effect of nonlinearity. In addition, the authors want to prepare the ground for the advent of new high-temperature materials. For the numerical examples presented comparison with reference solutions is made where available. Thus the present overview intends to impact a continuing discussion on the unification and integration of thermal and structural analyses methods as they apply to large and complex high-temperature composite shell structures under combined thermal and mechanical loading. In this respect it also intends to contribute to the on-going efforts of integrating thermal and structural engineering codes and the development of suitable interfaces. Future research trends are also identified.