With the development of magnetic resonance imaging techniques for acquiring diffusion tensor data from biological tissue, visualization of tensor data has become a new research focus. The diffusion tensor describes the directional dependence of water molecules' diffusion and can be represented by a three-by-three symmetric matrix. Visualization of second-order tensor fields is difficult because the data values have many degrees of freedom. Existing visualization techniques are best at portraying the tensor's properties over a two-dimensional field, or over a small subset of locations within a three-dimensional field. A means of visualizing the global structure in measured diffusion tensor data is needed. We propose the use of direct volume rendering, with novel approaches for the tensors' coloring, lighting, and opacity assignment. Hue-balls use a two-dimensional colormap on the unit sphere to illustrate the tensor's action as a linear operator. Lit-tensors provide a lighting model for tensors which includes as special cases both lit-lines (from streamline vector visualization) and standard Phong surface lighting. Together with an opacity assignment based on a novel two-dimensional barycentric space of anisotropy, these methods are shown to produce informative renderings of measured diffusion tensor data from the human brain.