Although the issues are not very controversial, the fusion of both the fields of heat conduction in solids and elasticity which results in the so-called field of dynamic thermoelasticity (both non-classical and classical), dates as far back as Maxwell (1867), and has long been a subject matter of widespread research activity and interest. Although routine thermomechanical problems are primarily influenced by classical effects, issues where non-classical influences may become important are also addressed. To date, numerous applications ranging from defense, aerospace to manufacturing related problems including routine mechanical, civil, nuclear and allied engineering applications influenced by thermal-structural interactions continue to pose significant challenges both from the underlying mechanics and from a computational viewpoint. Herein is first presented an overview of non-classical and classical dynamic thermoelasticity models and equations governing these situations. Subsequently, attention is focused on computational approaches for the modeling and analysis of various classes of problems encompassing thermal-structural interactions which can be broadly classified as: i) thermally-induced stress wave propagation problems, ii) thermally-induced dynamic (inertial type) problems, and iii) the general field of thermal stresses. A variety of illustrative numerical examples encompassing non-classical and classical influences are finally presented to provide an improved understanding of the behavior of thermal-structural problems via effective unified computational developments. This review article contains 142 references.