  Models of open inflation with a variable density parameter $\Omega$ provide
the most natural way to reconcile an open universe with inflation. The use of
anthropic principle is essential to derive observational predictions of such
models. I discuss how this principle can be used in a quantitative way to
determine the most probable value of $\Omega$. I also comment on recent work by
Hawking and Turok on quantum creation of open universes from nothing.
