Advanced structures, including Carbon Fiber Reinforced Polymer (CFRP) composites and lattice structures, have drawn significant attention due to their exceptional mechanical performance. However, their quality and mechanical performance can degrade because of defects introduced during manufacturing or in-service. This thesis proposes non-invasive electrical tomographic imaging techniques, electrical resistance tomography (ERT), electrical impedance tomography (EIT), and electrical capacitance tomography (ECT), for damage detection in advanced structures. These techniques leverage boundary measurements to reconstruct the interior electrical properties distribution of the advanced structures, such as electrical conductivity and permittivity, which are directly correlated to structural damage maps. However, classical electrical tomographic methods face challenges when applied to anisotropic CFRP composites and suffer from limited central sensitivity. To overcome these limitations, this thesis incorporated specific modifications, including the use of electrical conductivity tensors and normalized sensitivity maps. These enhancements improve the applicability of electrical tomographic methods on CFRP composites and lattice structures with complex geometries. Also, the use of smart paint and frequency-difference EIT was explored to enhance damage detection in painted advanced structures without the need for baseline measurements. Additionally, to increase computational efficiency for defect detection, machine learning methods are integrated with tomographic techniques. Simulation and experimental studies were conducted to evaluate the performance of the proposed techniques, and comparisons were made with classical solvers. The results demonstrate the effectiveness of the proposed ERT, EIT, and ECT methods in detecting damage in advanced structures. This comprehensive investigation provides valuable insights for damage detection in advanced structures, contributing to more efficient and effective inspection processes.