Searches for extra spatial dimensions remain among the most popular new
directions in our quest for physics beyond the Standard Model. High-energy
collider experiments of the current decade should be able to find an ultimate
answer to the question of their existence in a variety of models. Until the
start of the LHC in a few years, the Tevatron will remain the key player in
this quest. In this paper, we review the most recent results from the Tevatron
on searches for large, 1/TeV-size, and Randall-Sundrum extra spatial
dimensions, which have reached a new level of sensitivity and currently probe
the parameter space beyond the existing constraints. While no evidence for the
existence of extra dimensions has been found so far, an exciting discovery
might be just steps away.Comment: To appear in Proceedings of SLAC Summer Institute, 2004. An extended
version of the talk given on behalf of the CDF and D0 Collaboration