An overview of tensor valuations on lattice polytopes is provided composed of two contributions that began the development of the theory of these valuations; a characterization result preceded by a thorough study of the basis elements of the vector space of valuations. A complete classification, based on a joint paper with Monika Ludwig , is established of symmetric tensor valuations of rank up to eight that are translation covariant and intertwine the special linear group over the integers. The real-valued case was established by Betke & Kneser where it was shown that the only such valuations are the coefficients of the Ehrhart polynomial. The Ehrhart polynomial is generalized to the Ehrhart tensor polynomial with coefficients Ehrhart tensors. Extending the result of Betke & Kneser, it is shown that every tensor valuation with these properties is a combination of the Ehrhart tensors, for rank at most eight, which is shown to no longer hold true for rank nine. A new valuation that emerges in rank nine is described along with candidates for tensors of higher rank. Furthermore, the reciprocity theorems by Ehrhart & Macdonald are extended to tensor valuations. Based on a joint paper with Sören Berg and Katharina Jochemko , the Ehrhart tensors are investigated. Pick-type formulas are given, for the vector and matrix cases, in terms of triangulations of the given lattice polygon. The notion of the Ehrhart h*-polynomial is extended to h r-tensor polynomials and, for matrices, their coefficients are studied for positive semidefiniteness. In contrast to the classic h*-polynomial, the coefficients are not necessarily monotone with respect to inclusion. Nevertheless, positive semidefiniteness is proven in the planar case. Based on computational results, positive semidefiniteness of the coefficients in higher dimensions is conjectured. Furthermore, Hibi's palindromic theorem for reflexive polytopes is generalized to h r-tensor polynomials.