  We study the cluster categories arising from marked surfaces (with punctures
and non-empty boundaries). By constructing skewed-gentle algebras, we show that
there is a bijection between tagged curves and string objects. Applications
include interpreting dimensions of $\operatorname{Ext}^1$ as intersection
numbers of tagged curves and Auslander-Reiten translation as tagged rotation.
An important consequence is that the cluster(-tilting) exchange graphs of such
cluster categories are connected.
