Functional MRI (fMRI) at 7T and above provides improved Signal-to-Noise Ratio and Contrast-to-Noise Ratio compared to 3T acquisitions. In addition to the beneficial effects on spin polarization and magnetization of deoxyhemoglobin, the increased applied field also further magnetizes air and tissue. While the magnets themselves typically provide a static B field with sufficient spatial homogeneity, the diamagnetism of tissue and the paramagnetism of air causes local field deviations inside the human head. These spatially-varying field offsets (ΔB) cause image artifacts, especially in single shot EPI, including geometric distortion, signal dropout, and blurring. These effects are particularly strong near air-tissue interfaces such as the frontal sinus, and ear canals. Furthermore, if the field offsets are dynamically modulated through physiological processes such as respiration or motion, then the effect on the image time-series can be even more problematic. While post-processing methods have been developed to mitigate these effects, the ideal solution would be to reduce the ΔB variations at their source. Typically 7T scanners contain 2nd and some 3rd order spherical harmonic shim coil terms to cancel static ΔB variations of low spatial order. In this article, we will motivate the need for improved, higher-order compensation for B inhomogeneity and potentially add dynamic control of these fields. We discuss and compare several promising hardware approaches for static and dynamic B shimming using either higher-order spherical harmonic shim coils or multi-coil shim arrays as well as passive shimming approaches, and active variants such and adaptive current networks.