The material discussed in this monograph is too rich to be adequately sketched in a review of ordinary length. It shall, therefore, be sufficient to give an indication of the contents. The first chapter is devoted to a rigorous development of a very general plate model including the Mindlin-Timoshenko (MT) system, the Kirchhoff-plate, thermoelastic- and viscoelastic-plate models. The second chapter provides a general variational set-up, appropriate to cover all different dynamical systems discussed before. The third chapter, presumably the core of the study, is concerned with the Hilbert uniqueness method (HUM-) principle and with a priori energy estimates needed in order to apply this principle. The general (generalizable) avenue along which one proceeds is to first formulate the control system and its homogeneous reverse-adjoint.