Cluster algebras are commutative rings with a set of special generators that captures a rich combinatorial structure. First reviewing the basics on cluster algebras, we will describe certain configuration spaces of affine flags on marked surfaces and their associated cluster algebras studied by Fock and Goncharov since 2003. After that, we will observe and discuss limitations to this approach through an example, then describe a cluster structure arising from the configuration of vectors on a once-punctured polygon described by Fomin, Williams and Zelevinsky.