InGaN/GaN nanowire (NW) heterostructures grown by plasma assisted molecular beam epitaxy were studied in comparison to their GaN and InGaN counterparts. The InGaN/GaN heterostructure NWs are composed of a GaN NW, a thin InGaN shell, and a multifaceted InGaN cap wrapping the top part of the GaN NW. High-resolution transmission electron microscopy (HRTEM) images taken from different parts of a InGaN/GaN NW show a wurtzite structure of the GaN core and the epitaxial InGaN shell around it, while additional crystallographic domains are observed whithin the InGaN cap region. Large changes in the lattice parameter along the wire, from pure GaN to higher In concentration demonstrate the successful growth of a complex InGaN/GaN NW heterostructure. Photoluminescence (PL) spectra of these heterostructure NW ensembles show rather broad and intense emission peak at 2.1 eV. However, μ-PL …