Skin effect is usually a concern reserved for radio frequency design and for high current conductors used in utility power distribution. Proximity effect between adjacent conductors has traditionally been a concern for the design of magnetic windings and other applications involving wire bundles. The rise in the ubiquity of high speed bit streams and other signals of very wide bandwidth has broadened the range of applicable contexts and increased the need to account for such effects. This is especially true for transmission lines used to interconnect critical signal paths in applications ranging from microelectronic devices to the signal integrity of printed circuit traces and implementation of system cabling. Optimal conductor design is obviously fundamental to transmission line performance. Researchers have paid considerable attention to the topic but the results are scattered throughout the literature. This thesis collected information on extant conductor designs, and the theoretical considerations behind each solution. A detailed analysis of current flow in a conducting half-space was included as a foundation. The conductor types discussed were solid cylindrical, rectangular, ribbonoid, bimetallic, tubular, laminated, litz, and stranded constructions. Discussions of the performance of stranded shields and conductor roughness effects were included for completeness of understanding.