Three-dimensional topology-independent methods to look for global topology

The spacelike hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this spacelike hypersurface would imply that the apparently observable universe (the sphere of particle horizon radius) could contain several images of the single, physical Universe. Recent three-dimensional techniques for constraining and/or detecting this topology are reviewed. Initial applications of these techniques using x-ray bright clusters of galaxies and quasars imply tweak) candidates for a non-trivial topology.