We hereby report developments on the fabrication and characterization of epitaxial thin films of proton conducting Y-doped BaZrO3 (BZY) by pulsed laser deposition (PLD) on different single crystal substrates (MgO, GdScO3, SrTiO3, NdGaO3, LaAlO3 and sapphire) using Ni-free and 1% Ni-containing targets. Pure, high crystal quality epitaxial films of BZY are obtained on MgO and on perovskite-type substrates, despite the large lattice mismatch. The deposition conditions influence the morphology, cell parameters and chemical composition of the film, the oxygen partial pressure during film growth being the most determining. Film characterization was carried out using X-ray diffraction, transmission electron and atomic force microscopies, wavelength dispersive X-ray spectroscopy and angle-resolved X-ray photoelectron spectroscopy. All films show a slight tetragonal distortion that is not directly related to the substrate-induced strain. The proton conductivity of the films depends on deposition conditions and film thickness, and for the optimised conditions its total conductivity is slightly higher than the bulk conductivity of the target material (3 mS/cm at 600 degrees C, in wet 5% H-2/Ar). The conductivities are, however, more than one order of magnitude lower than the highest reported in literature and possible reasoning is elucidated in terms of local and extended defects in the films.