We discuss iterated function systems generated by finitely many con- tinuous self-maps on a compact metric space, with a focus on transitivity and min- imality properties. More specifically, we are interested in topological transitivity, fiberwise transitivity, minimality and total minimality. A number of results that clarify the relations between topological transitivity and fiberwise transitivity are included. Furthermore, we generalize the notion of regular periodic decomposition for topologically transitive maps, introduced by John Banks [1], to iterated function systems. We will focus on the existence of periodic decompositions for topologically transitive iterated function systems. Finally, we show that each minimal abelian iterated function system consisting of homeomorphisms on a connected compact metric space is totally minimal.

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