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The growth of spontaneous (catalyst-free) self-assembled and ordered (localized) III-Nitride nanocolumns (NCs) by Molecular Beam Epitaxy (MBE) is addressed, with emphasis on the nucleation process. In self-assembled NCs growth, nucleation proceeds via Volmer-Weber or Stranski-Krastanov mechanisms depending on the initial lattice mismatch between the NCs material and substrate. It is experimentally observed that a high initial mismatch (i.e. GaN on bare Si) leads to isolated, well defined NCs, whereas a smaller one (i.e. GaN on AlN buffered Si) produces a mixture of NCs and a "faceted matrix" of continuous, rough material. A successful localized growth on patterned or masked (nanoholes) substrates depends critically on a balance between metal atoms diffusion and desorption, that are both strongly influenced by the growth temperature and the III/V ratio. A proper selection of the growth conditions leads to a reasonable growth rate within the nanoholes (mask) whereas avoiding NCs nucleation on the mask (selectivity). Self-assembled III-Nitride polar GaN and InN NCs have been successfully grown by many researchers, though little work has been done on non-polar NCs. Here we present results on the self-assembled growth of non-polar (a-plane) InN NCs on m-plane GaN/r-plane Al2O3 templates. A well defined a-plane orientation is determined by HR-TEM and from the dependence of the E2 Raman mode with the polarization angle. HR-SEM pictures reveal top NC surfaces showing a- and m- plane facets. A low-temperature PL emission energy of 0.69 eV, a typical of very high quality material, is observed. Though self-assembled NCs are quite useful to understand the basic growth mechanisms and material properties, the growth of ordered arrays of NCs is essential to fabricate real devices, like LEDs and detectors, because of the need of homogeneous geometry and characteristics of individual nanodevices. Details will be given on the use of thin Ti masks with nanoholes of different diameter and pitch and on the specific conditions for localized growth, far from those to grow self-assembled NCs. Different approaches of ordered arrays will be revised with emphasis on the applications to efficient optoelectronic devices, like phosphor-free white LEDs, and multijunction solar cells.