  I give a brief informal introduction to the idea and tests of large extra
dimensions, focusing on the case in which the space-time manifold has a direct
product structure. I then describe some attractive implementations in which the
internal space comprises a compact hyperbolic manifold. This construction
yields an exponential hierarchy between the usual Planck scale and the true
fundamental scale of physics by tuning only ${\cal O}(1)$ coefficients, since
the linear size of the internal space remains small. In addition, this allows
an early universe cosmology with normal evolution up to substantial
temperatures, and completely evades astrophysical constraints.
