AlN is one of the most important optoelectronic materials in the wide hand gap LII-V semiconductors because of its wide and tunable energy band gap in conjunction with other nitrides, high thermal conductivity, doping capabilities, and high hardness. The proposed optoelectronic devices require high quality epitaxial films on various substrates. Here, we present our recent work on the fabrication of high quality epitaxial AlN films on Al2O3(0001), Si(lll) and 6H-SiC(0001) by pulsed laser deposition (PLD). The PLD is a nonequilibrium technique where thin film growth temperature can be reduced by more than 250-350 degrees C and epitaxial films comparable in quality to MOCVD (equilibrium technique) obtained. The laser fluence and the substrate temperature were found to be crucial processing parameters for the formation of high quality monocrystalline AlN films. The AlN films deposited above 750 degrees C and laser energy densities of 2-3 J cm(-2) were found to be epitaxial with c-axis normal to substrate plane. The X-ray rocking curve of epitaxial films on sapphire and SiC yielded full-width-at-half-maximum of similar to 0.06-0.07 degrees. The transmission electron microscopy also revealed that the films were epitaxial with an orientational relationship of AlN[0001]parallel to Al2O3[0001], AlN[0001]parallel to Si[111], AlN[0001]parallel to SiC[0001] and in-plane alignment of AlN[<(1)over bar 2><(1)over bar 0>]parallel to Al2O3[<0(1)over bar 10>], AlN[<10(1)over bar 0>]parallel to Al2O3[<(2)over bar 110>], AlN[<2(11)over bar 0>]parallel to Si[01(1) over bar] and AlN[<0(1)over bar 10>]parallel to SiC[<0(1)over bar 10>]. The optical absorption edge measured by UV-visible spectroscopy for the epitaxial AlN film on sapphire was sharp and the band gap was found to be 6.1 eV. The electrical resistivity of the films was about 5-6 x 10(13) Omega cm(-1) with a breakdown field of 5 x 10(6) V cm(-1).