Topology optimization (TO) of complex structures, especially at fine discretizations and in multiscale settings, is often limited by the high dimensionality of design variables and the associated computational cost. In this talk, we present a unified reduced-order framework for TO based on transformed tensor decomposition and Proper Generalized Decomposition (PGD) techniques, targeting at both single-scale and multiscale TO problems. First, a transformed tensor decomposition method is introduced for density-based TO. A nonlinear transform is applied to the density variable to regulate its admissible range and improve numerical robustness. The transformed density field is then approximated by a finite sum of modes, each expressed in a variable-separated form. This representation significantly reduces the number of effective design variables and reduces the computational cost per optimization iteration. Numerical examples demonstrate that the proposed method not only accelerates convergence, but also effectively alleviates classical numerical issues such as checkerboard patterns and mesh dependency. Second, a PGD-based surrogate modeling strategy is developed for parametrized numerical homogenization and multiscale TO. The surrogate model constructs an explicit mapping from microstructural geometric parameters to the effective elasticity tensor without the need for offline sampling or large data storage. Owing to the variable-separated representation, the proposed PGD surrogate achieves high computational efficiency and accuracy. It is then integrated into a multiscale TO framework under a prescribed volume fraction constraint of the matrix material. Several examples are presented to validate the accuracy, efficiency, and robustness of the proposed approaches. The results show that tensor decomposition and PGD-based reduced-order models provide an effective and scalable solution for TO problems. This work highlights the potential of tensor-based model reduction techniques in advancing computational mechanics and structural optimization.