  We address some issues of topological defect inflation. (1) We clarify the
causal structure of an inflating magnetic monopole. The spacetime diagram shows
explicitly that this model is free from the ``graceful exit'' problem, while
the monopole itself undergoes ``eternal inflation''. (2) We extend the study of
inflating topological defects to Brans-Dicke gravity. Contrary to the case of
Einstein gravity, any inflating monopole eventually shrinks and takes a stable
configuration. (3) We reanalyze chaotic inflation with a non-minimally coupled
massive scalar field. We find a new solution of domain wall inflation, which
relaxes constraints on the coupling constant for successful inflation.
