Microtubules, protein polymers composed of tubulin hetero-dimers, are important components of the cytoskeleton of eukaryotic cells, performing multiple subcellular functions. Due to their central role in cell division, they are important oncologic targets in pharmacology. They also hold promise for possible applications in bio-nanotechnology. We study microtubules computationally and analytically using atomic resolution structures of their constituent units: tubulin dimers. The C-terminal regions of tubulin are important in the regulation of microtubule assembly, as attachment points for microtubule associated proteins and in the binding of motor proteins, e.g. kinesin. We will briefly review biochemical properties of tubulin and microtubules and discuss a number of their unique biophysical properties: polymerization kinetics, elastic, electrostatic and conductive characteristics. Molecular models of elastic properties of microtubules and their estimates lead to anisotropic elastic moduli which were observed in recent experiments. Based on the atomic resolution structures of tubulin, values of net charge, dipole moments and spatial charge distribution were obtained and physical consequences of these results will be discussed. We will also describe ionic conductivity experiments performed with our collaborators and the results of our transmission line modeling. Under appropriate conditions, tubulin is able to nucleate silver, gold, platinum and palladium nanoparticles forming metallic arrays on microtubule surfaces. By further particle growth, a quasi-continuous coating can be obtained resulting in metallized protein nanowires which can be assembled into circuits. Such an organization of functional 2D and 3D protein assemblies provides a potential approach to develop electronic devices with novel I-V characteristics and attractive physical and biochemical properties such as self-organization.