  A recently introduced framework for the compactification of supersymmetric
string theory involving noncritical manifolds of complex dimension
$2k+D_{crit}$, $k\geq 1$, is reviewed. These higher dimensional manifolds are
spaces with quantized positive Ricci curvature and therefore do not, a priori,
describe consistent string vacua. It is nevertheless possible to derive from
these manifolds the massless spectra of critical string groundstates. For a
subclass of these noncritical theories it is also possible to explicitly
construct Calabi--Yau manifolds from the higher dimensional spaces. Thus the
new class of theories makes contact with the standard framework of string
compactification. This class of manifolds is more general than that of
Calabi--Yau manifolds because it contains spaces which correspond to critical
string vacua with no K\"ahler deformations, i.e. no antigenerations, hence
providing mirrors of rigid Calabi--Yau manifolds. The constructions reviewed
here lead to new insight into the relation between exactly solvable models and
their mean field theories on the one hand and Calabi--Yau manifolds on the
other, leading, for instance, to a modification of Gepner's conjecture. They
also raise fundamental questions about the Kaluza--Klein concept of string
compactification, in particular regarding the r\^{o}le played by the dimension
of the internal theories.
