The discovery of high-T c superconductivity in Fe-based superconductors pioneered by Kamihara et al (2008 J. Am. Chem. Soc. 130 3296-7) has triggered worldwide research efforts in both science and technology. High-quality epitaxial thin films of Fe-based superconductors are required to develop Fe-based superconducting devices, such as Josephson junctions and superconducting quantum interference devices, and also to develop Fe-based superconducting coated conductors (tapes) with high J c under strong magnetic fields. Epitaxial films are also required for basic research to explore the intrinsic properties of Fe-based superconductors, since sizable bulk single crystals are difficult to grow for some of the Fe-based superconductors such as LnFeAs(O,F) (Ln: lanthanoid element). There are several families of Fe-based superconductors: Fe(Se,Te) with T c ∼15 K, LiFeAs with T c ∼18 K, (Ae,K)Fe 2 As 2 (Ae=alkaline earth element) with T c ∼38 K for Ae=Ba, and LnFeAs(O,F) with T c ∼55 K for Ln=Nd or Sm. Increasing the number of elements in compounds, the T c becomes higher. Simultaneously, thin-film growth becomes more difficult in principle, and it was not imagined at the beginning of the research that thin-film growth of five-element compounds, LnFeAs(O,F), could be realized quickly. At present, T c as high as 58 K exceeding the highest T c ever reported for bulk samples and high critical current density (J c ) over 3 MA cm −2 are obtained in SmFeAs(O,F). In this topical review, we present an overview of the progress in thin-film growth of representative Fe-based superconductors over a decade, including a detailed description of the growth recipes for each family using molecular beam epitaxy or pulsed laser deposition. Furthermore, we present recent hot topics, such as monolayer FeSe with T c much higher than bulk T c , though how high T c can be reached has not been established. Other examples making use of the advantages specific to thin films such as stabilization of quasi-equilibrium phases, enhancement of T c by epitaxial strain, etc will also be described.