The electromigration effect within current-density-stressed signal and power lines is an ubiquitous and increasingly important reliability and design problem in sub-micron IC designs. It is therefore necessary to consider electromigration-related design parameters as early as possible in the physical design flow. In this tutorial, we first give an introduction into the electromigration problem and its relationship to current density and temperature. Physical design parameters that affect current density are presented next. We then focus on various distinctive methodologies that allow the electromigration problem to be addressed directly during physical design and verification of both analog and digital circuits. We also present and discuss commercial applications of these electromigration-aware methodologies.