Two efficient implementations of 3D and 2.5D modeling and inversion are presented to be applicable to large-scale transient electromagnetic (TEM) method explorations. The key novel features are (1) forward response and Jacobian calculations are implemented using the octree-based finite-element method, (2) a mirror approach is used to build a 2.5D inversion scheme for further efficiency, and (3) a flexible link between the forward mesh and inversion model is applied on 3D and 2.5D schemes based on the voxel formulation. We compare the performance of the new implementations with 3D modeling using tetrahedral meshes, with respect to speed and memory requirements. The 3D octree algorithm requires less than 1/3 of the computational time compared with a 3D tetrahedral scheme for equivalent accuracy. The 2.5D octree algorithm further speeds up the process by reducing the computational time by another factor of two. The inversion uses the Levenberg-Marquart approach minimizing the least-squares criterion of the objective function. We determine the utility of our inversion approach on a synthetic example and a field example. In the synthetic example, the 3D octree inversion result finds superior resolution of a 3D anomaly compared with a 1D result, whereas the 2.5D inversion result is, expectedly, between the 1D and 3D results, but with favorable computational expenses compared with the full 3D solution. The field data set contains 200 soundings, and we perform a 3D inversion on the full survey. A 24-sounding section is then selected for the 2.5D inversion. The 2.5D inversion result finds resistivity features similar to the 3D inversion result at the selected profile. Hence, we conclude that the presented implementations are capable of handling relatively large TEM surveys on modern computational platforms. This could be smaller subsets of production-size surveys where 2D and 3D effects are pronounced.