Multiferroic materials have received an astonishing attention in the last decades due to expectations that potential coupling between distinct ferroic orders could inspire new applications and new device concepts. As a result, a new knowledge on coupling mechanisms and materials science has dramatically emerged. Multiferroic RMnO3 perovskites are central to this progress providing a suitable platform to tailor spin-spin and spin-lattice interactions. With views towards applications, development of thin films of multiferroic materials have also progressed enormously and nowadays thin film manganites are available with properties mimicking those of bulk compounds. Here we review achievements on the growth and characterization of magnetic and ferroelectric properties of hexagonal and orthorhombic RMnO3 epitaxial thin films, discuss some challenging issues and we suggest some guidelines for future research and developments.