In addition to the three-dimensional space that we are familiar with, the space might extend in other
compact dimensions. The upper bound set by various experiments and  phenomenological constraints
on the size of  the extra dimensions depends on what sort of fields can propagate in these dimensions.
The most general bound comes from measurements of the gravitational force, and is of order 1 mm.
Regions of the compact space accessible to the Standard  Model particles are constrained by collider
experiments to have sizes below 10^{-17} cm.

Various signals associated with extra dimensions could be within the reach in the  Run II of the Fermilab
Tevatron. These issues are addressed by the Workshop on New Strong Dynamics.

Bibliography on:
Dimensions accessible to the Standard Model gauge bosons.
Dimensions accessible only to gravity.
Extra dimensions at the Tevatron.
Electroweak  symmetry breaking  and flavor from compact dimensions.