We present recent advances in FFT-based formulations for the prediction of the micromechanical response and microstructure evolution of polycrystalline materials. This methodology originally proposed at the turn of the century for composites [1] and extended to polycrystalline materials, provides a significant increase in numerical efficiency compared with Finite Element-based formulations. Moreover, FFT-based methods can use direct input from and/or their output directly compared with large voxelized microstructural datasets measured on deformed polycrystals. Specifically, we have adapted our recent large-strain elasto-viscoplastic FFT-based formulation (LS-EVP-FFT) [2] to overcome two previous limitations of FFT-based formulations, i.e., the lack for geometric accuracy to represent general interfaces using voxelized microstructures, and the imposition of periodic boundary conditions. Extending the use of the “conformal” deformation gradient field—proposed in [2] as part of the multiplicative decomposition of the total deformation gradient using Lagrangian mechanics for LS-EVP problems—allowed us to consider geometrically accurate internal boundaries, as well as displacement boundary conditions applied to non-periodic microstructures. We will present illustrative examples of how these new features enable more accurate predictions of the micromechanical response of plastically deforming polycrystalline materials. [1] Moulinec, H., Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure. CMAME 157, 69, (1998). [2] M. Zecevic, R.A. Lebensohn and L. Capolungo: "New large-strain Fast Fourier Transform-based formulation and its application to strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials". Mechanics of Materials, 166, 104208 (2022).