The structural and electronic properties of core-shell, eutectic, biaxial and superlattice GaN-AlN nanowires were studied through density functional theory computations. Due to more surface dangling bonds, nanowires with smaller diameters are energetically unfavorable. For the GaN-AlN heterostructure nanowires, their electronic properties highly depend on the GaN content, axial strain, configuration, and size. The valence bands are less affected by the GaN content, while the conduction bands depend on it. Hydrogen-passivated nanowires have much larger band gaps than their counterparts, since the surface states are removed by saturating the dangling bonds with hydrogen atoms. Moreover, due to multiple quantum-well structures, the confined electrons (holes) of superlattice nanowires become more localized and the difference of the mobility between the electron and hole becomes less apparent if the width of the barrier is larger. These findings are of value for better understanding heterostructure nanowires and their potential utilization.