Advanced 3D microstructural analysis in natural sciences and engineering depends ever more on modern data acquisition and imaging technologies such as micro-computed or synchrotron tomography and interactive visualization. The acquired high-resolution volume data sets have sizes in the order of tens to hundreds of GBs, and typically exhibit spatially complex internal structures. Such large structural volume data sets represent a grand challenge to be explored, analyzed and interpreted by means of interactive visualization, since the amount of data to be rendered is typically far beyond the current performance limits of interactive graphics systems. As a new approach to tackle this bottleneck problem, we employ higher-order tensor approximations (TAs). We demonstrate the power of TA to represent, and focus on, structural features in volume data. We show that TA yields a high data reduction at competitive rate distortion and that, at the same time, it provides a natural means for multiscale volume feature representation.