Strange attractors generated by three-dimensional dynamical systems can be classified. The classification has four levels of structure: 1.\tBasis sets of unstable periodic orbits (UPOs) 2.\tBranched manifolds that contain the UPOs 3.\tBounding tori that contain branched manifolds 4.\tExtrinsic embedding of tori in R3. The classification is topological. This means that it is expressed in terms of integers. Procedures have been developed for extracting these inte-gers from experimental data. We review each level in this hierarchy of structures and describe (with examples) how these signatures have been extracted from experimental data. We point out the questions that have been raised and that remain to be answered for three-dimensional strange attractors. We point out the opportunities that exist for applying topolog-ical methods to the description and analysis of higher dimensional strange attractors.