With technology scaling, on-chip power densities are growing steadily, leading to the point where temperature has become an important consideration in the design of electrical circuits. This paper overviews several methods for the analysis and optimization of thermal effects in integrated circuits. Thermal analysis may be carried out efficiently through the use of finite difference methods, finite element methods, or Green function based methods, each of which provides different accuracy-computation tradeoffs, and the paper begins by surveying these. Next, we overview a restricted set of thermal optimization methods, specifically, placement techniques for thermal heat-spreading, and then we conclude by summarizing a set of future directions in electrothermal design.