Nanowires have received significant interest from the scientific community due to their potential for electronic applications. This thesis is devoted to understanding the growth mechanisms and physical properties of a variety of nanowire structures grown by molecular beam epitaxy (MBE). The study described in this thesis can be subdivided into four main topics: the formation of self-assembled eutectic nanoparticles, the formation of single crystal semiconducting nanowires, the formation of heterostructured semiconducting nanowires, and the magnetic properties of GaAs/Fe core/shell nanowires. As a part of this study, I explore the growth mechanisms behind the formation of eutectic nanoparticles which are used as a catalyst to fabricate nanowires by molecular MBE. The morphology of the nanowires is very closely related to the morphology of the nanoparticle catalysts, and therefore is of considerable interest for the study of the formation of nanowires. From this study, I find that the size and spatial distributions of self-assembled nanoparticles are strongly influenced by the growth conditions.  The study of the formation of single crystal semiconducting nanowires examines the growth mechanisms, morphology, and crystal structure of GaAs, ZnTe, ZnSe, and Ge nanowires grown on a variety of substrates by MBE. This study employs electron microscopy to study growth mechanisms responsible for the nanowire crystal structure and shape. As a part of this study we find that the migration of surface adatoms contributes significantly to the nanowire morphology. Layered semiconducting structures can have interesting properties that are useful for producing a variety of electronic, magnetic, and optoelectronic devices. The study of the formation of heterostructured semiconducting nanowires explores several core/shell and axial heterostructures. As a part of this study, we observe several growth mechanisms which impede the formation of high quality layered structures, as well as several that promote high quality layered structures.  Finally, we examine the magnetic properties of GaAs/Fe core/shell nanowires. To overcome the various challenges associated with studying nanoscale magnetic crystals, many advanced experimental techniques were employed in this thesis. A study of the magnetic behavior of single GaAs/Fe core/shell nanowires both with and without the presence of an externally applied magnetic field is presented.