Several III-V nanowire materials systems exhibit features of polytypism, which is a kind of polymorphism, where the polymorphs differ only in the layer stacking sequence. In bulk, all III-V semiconductors, except nitrides, exhibit the zinc blende structure (3C polytype). However, when these materials are grown as nanowires, they often exhibit a seemingly random crystal structure and by tuning the growth parameters, more or less pure 3C or 2H can be fabricated. Sometimes often higher order polytypes, such as 4H and 6H form. In order to use III-V nanowires in electronic and optoelectronic applications, it is of highest importance to control and possibly also take advantage of the polytypism. In our current investigations, we take a classical nucleation approach to explain the phenomenon of polytypism in metal particle-seeded III-V nanowires, including polytypes up to 6H. In order to describe the formation of higher order polytypes, interaction between the stacked layers, which goes beyond nearest neighbor interactions must be taken into account. For this purpose we use the axial next nearest neighbor Ising (ANNNI) model, which I introduce before I describe our specific approach. In the ANNNI model, the stacking sequence is treated as a sequence of generalized spins and different sequences give different total energies, depending on the interlayer interaction parameters. The total energies for several polytypes can be calculated by ab initio techniques for any given material. In addition, from the total energy expressions a phase diagram can be constructed, in which the ab initio results can be visualized. Using this approach, it has been shown that 6H is the most stable SiC polytype and it has been verified that the III-V semiconductors are very stable in 3C. Another, more kinetic approach to the ANNNI modeling of polytypism is to keep track of the incremental energy change due to the addition of single layers. This approach has been used to explain the preference of SiC to grow in the 3C polytype during CVD. In our approach to polytypism in nanowires, we use the ANNNI model to express the interface energy between the forming nucleus and the underlying layers for the 3C, 6H, 4H, and 2H polytypes. I will show how to combine this interface energy with our nucleation theoretical framework and describe how we can use this model to calculate the formation probabilities of these four polytypes as functions of supersaturation. Depending on the interaction parameters, the range of attainable polytypes as a function of supersaturation can vary, and this can be graphically represented. I will introduce such polytype attainability diagrams and discuss their experimental relevance.