Abstract. We review and illustrate the impact of TEM on the study of nanowires of nonnitride III-V semiconductors, with particular emphasis on the understanding of the thermodynamics and kinetics of their formation assisted by nano-sized catalyst particles. Besides providing basic information about the morphology of the nanowires and their growth rate as a function of diameter, TEM offers insights into the peculiar crystalline structure that they adopt. We discuss the formation of the unusual wurtzite hexagonal crystalline phase and that of planar stacking defects in these nanowires and show that they are kinetically controlled. We also demonstrate the transformation of wurtzite into cubic sphalerite upon epitaxial burying of the nanowires. Nanowires are particularly interesting in that they allow the fabrication of precisely positioned quantum dots with well-defined geometries. In this respect, we discuss the formation of strained quantum-size inclusions in nanowires, their critical dimensions and the kinetic and thermodynamic factors governing the changes of the crystalline structure that sometimes occur around a hetero-interface.