  ( to appear in: Proceedings of the Nishonomiya Yukawa Memorial Symposium
Edited by M. Sasaki) There are several models for generating fluctuations in an
open universe that are compatible with the microwave background fluctuations
detected by COBE {\it and} observations of large scale structure. Topological
defects, such as strings and textures, appear to be more successful in a
low-$\Omega$ model than in an $\Omega = 1$ model. These models predict that the
cosmic microwave background (CMB) fluctuations are non-Gaussian with
distinctive signatures that may lead to their confirmation. If there exists a
mechanism for generating scale invariant mass fluctuations, $(\delta M/M)^2
\propto M^{-4/3}$, then these models are also compatible with COBE. Both models
predict mass fluctuations on the 8/h Mpc scale, $\sigma_8$, $\sim 0.5 - 1$ for
$\Omega h \sim 0.2 - 0.3$. A variety of observations of large-scale structure,
clusters and galaxies, as well as the age problem, suggest that the
low-$\Omega$ models are attractive.
