Visualization of 3D, unsteady (4D) flow is very difficult due to both perceptual challenges and the large size of 4D vector field data. Here, we describe the use of integral surfaces for visualization of CFD simulation data. By "integral" surfaces we mean surfaces based on massless particles that are integrated according to the underlying flow. Traditionally, in-tegral curves, e.g., streamlines, pathlines, and streaklines are used to visualize 3D and 4D flow. However, integral surfaces offer clear benefits over integral curves when visualizing flow. Despite the clear benefits that stream, path, and streak surfaces bring when visualiz-ing 4D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of integral surface construction algorithms. We introduce algorithms for the construction of stream, path, and streak surfaces that are fast and do not rely on any complicated data structures or surface parametrization. Our surface construction algorithms generate the surfaces using a quadrangular mesh. The algorithms can be applied to large data sets because they are based on local operations performed on quad primitives. The algorithms offer a combination of speed for exploration of 3D, unsteady flow and high precision. Thus they are suitable for inclusion into any visualization application. We demon-strate the techniques on a series of simulation data sets and show a number of benefits that stem naturally from them. We also introduce interaction techniques in order to address the perceptual challenges associated with visualizing 3D, time-dependent CFD simulation data.