Volume rendering is a technique for visualizing sampled scalar fields of three spatial dimensions without fitting geometric primitives to the data. A color and a partial transparency are computed for each data sample, and images are formed by blending together contributions made by samples projecting to the same pixel on the picture plane. Quantization and aliasing artifacts are reduced by avoiding thresholding during data classification and by carefully resampling the data during projection. This thesis presents an image-order volume rendering algorithm, demonstrates that it generates images of comparable quality to existing object-order algorithms, and offers several improvements. In particular, methods are presented for displaying isovalue contour surfaces and region boundary surfaces, for rendering mixtures of analytically defined geometry and sampled fields, and for adding shadows and textures. Three techniques for reducing rendering cost are also presented: hierarchical spatial enumeration, adaptive termination of ray tracing, and adaptive image sampling. Case studies from two applications are given: medical imaging and molecular graphics.