Since Cu exhibits the highest electrical conductivity among base metals and common metals, pure Cu and dilute Cu alloys are widely used as functional materials for electrical components and power transmission materials. It is also expected that in the future, conductive pure Cu and Cu alloys will continue to be used according to the desired properties by understanding inherent characteristics of pure Cu and Cu alloys. This paper reviews factors such as the contribution of lattice defects and solute elements to the electrical conductivity of pure copper, and factors affecting strengthening processes such as precipitation hardening, solid solution hardening, and work hardening in dilute Cu alloys. In precipitation hardening, the type and amount of alloying elements added and the precipitation treatment are adjusted, but softening of the Cu alloy due to overaging must be avoided. In solid solution hardening, the type and amount of alloying elements are also optimized, often in combination with work hardening. Although work hardening generally results in changes in elongation and strength after processing, the decrease in electrical conductivity due to dislocations is small. Therefore, it is effective to combine work hardening with solid solution hardening and other processes. Microstructural characterization using analytical techniques have been conducted to elucidate the electrical conductivity and strengthening mechanisms of these alloys. Their findings are useful in controlling the conductive and mechanical properties of advance Cu alloys. This review also demonstrates the usefulness of these characterization methods.