We directly image the interior of GaAs/AlGaAs axial and radial nanowire heterostructures with atomic-scale resolution using scanning tunneling microscopy. We show that formation of monolayer sharp and smooth axial interfaces are possible even by vapor-phase epitaxy. However, we also find that instability of the ternary alloys formed in the Au seed fundamentally limits axial heterostructure control, inducing large segment asymmetries. We study radial core-shell nanowires, imaging even ultrathin submonolayer shells. We demonstrate how large twinning-induced morphological defects at the wire surfaces can be removed, ensuring the formation of wires with atomically flat sides.