High gain, planar array antennas which operate at millimetre wave frequencies, and can be mass produced at low cost, are desired by industry. The design of such arrays continues to be academically challenging. A literature review was conducted covering patents and papers describing antenna arrays either operating at, or suitable for operation at, millimetre wave frequencies. Four presently under exploited technology types were identified. Two of the under exploited technologies were investigated. Both small and medium sized arrays of non-radiating edge fed microstrip patches were built up in a consistent process. The design of the patch and 1 x 2 subarray were shown to affect the radiation pattern behaviour of 16 x 16 arrays. The placement of nulls in the 2 x 2 subarray radiation patterns proved critical to the mitigation of grating lobes, which were a source of directivity loss. A considerable difference in directivity characteristics across 10% bandwidth was found between in phase and 180 feeding within the 2 x 2 subarrays. An optimised 180 fed 4 x 4 subarray presented an improvement over prior work. Changing the boundary conditions at the juncture of the base and rim of the cavity of short backfire antennas was found to alter the directivity. Large diameter short backfire antennas with choked, inclined and curved junctures produced high directivity. A readily machinable design was used in a small array, to demonstrate its utility as a high aperture efficiency array element. The results are of importance to the future development of low cost, planar or quasi-planar antenna arrays, particularly at millimetre wave frequencies.