Ultra High Field (UHF) MRI requires improved gradient and shim performance to fully realize the promised gains (SNR as well as spatial, spectral, diffusion resolution) that higher main magnetic fields offer. Both the more challenging UHF environment by itself, as well as the higher currents used in high performance coils, require a deeper understanding combined with sophisticated engineering modeling and construction, to optimize gradient and shim hardware for safe operation and for highest image quality. This review summarizes the basics of gradient and shim technologies, and outlines a number of UHF-related challenges and solutions. In particular, Lorentz forces, vibroacoustics, eddy currents, and peripheral nerve stimulation are discussed. Several promising UHF-relevant gradient concepts are described, including insertable gradient coils aimed at higher performance neuroimaging.