Molecular beam epitaxy is used for the synthesis of catalyst-free GaAs nanowires and related quantum heterostructures. After growth of the nanowire GaAs core, the conditions are changed in situ towards standard MBE planar growth in order to obtain quantum heterostructures on the facets of the nanowires. Depending on the nanowire orientation, different geometries of the quantum heterostructures are obtained. This growth method is fully characterized by high resolution and scanning transmission electron microscopy and Z-contrast electron tomography. The growth conditions are also tuned for the optimization and homogeneity of the optical properties. The feedback of these analyses allows the tuning of the growth conditions according to the required optical properties. This work is the basis for obtaining a new generation of devices based on the heterostructures existing on the nanowire facets.