The growth conditions to achieve group-III-nitride nanocolumns and nanocolumnar heterostructures by plasma-assisted molecular beam epitaxy are studied. The evolution of the nanocolumnar morphology with the growth conditions is determined for (Ga,Al)N and (In,Ga)N nanocolumns. The mechanisms behind the nanocolumnar growth under high N-rich conditions are clarified in the sense that no seeding or catalysts are required, as it is the case in the vapour-liquid-solid model that applies to most nanocolumns grown by metal organic chemical vapour deposition, either with group-III nitrides, II -VI or III -V compounds. Some examples of nanocolumnar heterostructures are given, like quantum disks and cylindrical nanocavities. Preliminary results on the growth of arrays of ordered GaN nanocolumns are reported.