Three-dimensional gradient echo (GRE) is the main workhorse sequence used for susceptibility weighted imaging (SWI), quantitative susceptibility mapping (QSM), and susceptibility tensor imaging (STI). Achieving optimal phase signal-to-noise ratio requires late echo times, thus necessitating a long repetition time (TR). Combined with the large encoding burden of whole-brain coverage with high resolution, this leads to increased scan time. Further, the dipole kernel relating the tissue phase to the underlying susceptibility distribution undersamples the frequency content of the susceptibility map. Scans at multiple head orientations along with calculation of susceptibility through multi-orientation sampling (COSMOS) are one way to effectively mitigate this issue. Additionally, STI requires a minimum of 6 head orientations to solve for the independent tensor elements in each voxel. The requirements of high-resolution imaging with long TR at multiple orientations substantially lengthen the acquisition of COSMOS and STI. The goal of this work is to dramatically speed up susceptibility mapping at multiple head orientations. We demonstrate highly efficient acquisition using 3D-GRE with Wave CAIPI and dramatically reduce the acquisition time of these protocols. Using R = 15-fold acceleration with Wave-CAIPI permits acquisition per head orientation in 90 s at 1.1 mm isotropic resolution, and 5: 35 min at 0.5 mm isotropic resolution. Since Wave-CAIPI fully harnesses the 3D spatial encoding capability of receive arrays, the maximum g-factor noise amplification remains below 1.30 at 3T and 1.12 at 7T. This allows a 30-min exam for STI with 12 orientations, thus paving the way to its clinical application. (C) 2015 Elsevier Inc. All rights reserved.