  We study conformal defects in two important examples of string theory
orbifolds. First, we show that topological defects in the language of
Landau-Ginzburg models carry information about the RG flow between the
non-compact orbifolds $\mathbb{C}/\mathbb{Z}_d$. Such defects are shown to
correctly implement the bulk-induced RG flow on the boundary. Secondly, we
study what the possible conformal defects are between the $c=1$ bosonic 2D
conformal field theories with target space $S^1/\mathbb{Z}_2$. The defects
cataloged here are obtained from boundary states corresponding to D-branes in
the $c=2$ free theory with target space $S^1/\mathbb{Z}_2 \times
S^1/\mathbb{Z}_2$. Via the unfolding procedure, such boundary states are later
mapped to defects between the circle orbifolds. Furthermore, we compute the
algebra of the topological class of defects at different radii.
