High quality Ga-face and N-face AlGaN/GaN based heterostructures have been grown by plasma induced molecular beam epitaxy. By using Ga-face material we are able to fabricate conventional heterojunction field effect transistors. Because the N-face material confines electrons at a different heterojunction, the resulting transistors are called inverted. The Ga-face structures use a high temperature AIN nucleation layer to establish the polarity. Structures from these materials, relying only on polarization induced interface charge effects to create the two-dimensional electron gases, are used to confirm the polarity of the material as well as test the electrical properties of the layers. The resulting sheet concentrations of the two dimensional electron gases agree very well with the piezoelectric theory for this materials system. Hall mobilities of the two-dimensional gases for the N-face structures are as high as 1150 cm2/Vs and 3440 cm2/Vs for 300 K and 77 K respectively, while the Ga-face structures yield room temperature mobilities of 1190 cm2/Vs. Both structures were then fabricated into transistors and characterized. The inverted transistors, which were fabricated from the N-face material, yielded a maximum transconductance of 130 mS/mm and a current density of 905 mA/mm. Microwave measurements gave an ft of 7 GHz and an fmax of 12 GHz for a gate length of 1 μm. The normal transistors, fabricated from the Ga-face material, produced a maximum transconductance of 247 mS/mm and a current density of 938 mA/mm. Microwave measurements gave an ft of 50 GHz and an fmax of 97 GHz for a gate length of 0.25 μm. This shows that using plasma induced molecular beam epitaxy N-face and Ga(A1)-face AlGaN/GaN heterostructures can be grown with structural and electrical properties very suitable for high power field effect transistors.