Due to recent advances in resistivity well logging theory and practice, new triaxial induction tools sensitive to resistivity anisotropy have been developed. We have used the new sensitivities of these tools and developed 1D-3D inversion schemes capable to reveal details of highly laminated shale reservoirs. The ability to simulate responses of the new tools to arbitrary anisotropic 3D media is key to their successful application. We have examined a new fast 1D electromagnetic modeling method to simulate triaxial logging tool responses. The method is used as a forward engine for a new 1D inversion scheme for anisotropic formation parameters. An important new feature of the modeling method is its ability to model new tool responses to biaxial anisotropic medium, whose anisotropy tensor has up to three different principal values. This feature is particularly useful to evaluate anisotropic and fractured formations. We have also developed a universal medium-independent 3D modeling technique that can simulate new-generation tool responses in arbitrary 3D media including fracturing, and we used it as a full 3D inversion engine. Synthetic responses and several 1D-3D inversion results for a practical triaxial induction tool illustrate new features of the resistivity logs and their applications. The new 3D inversion does not require any preprocessing borehole correction, which can introduce significant errors at bed boundaries and in thin laminations. As a result, a higher spatial resolution of the tool can be provided. The new method was used to demonstrate and exploit high sensitivities of triaxial tensor measurement to all three principal values of the conductivity tensor.