We review the rapidly evolving efforts to analyze, model, simulate, and engineer genetic and biochemical information processing systems within living cells. We begin by showing that the fundamental elements of information processing in electronic and genetic systems are strikingly similar, and follow this theme through a review of efforts to create synthetic genetic circuits. In particular, we describe and review the "silicon mimetic" approach, where genetic circuits are engineered to mimic the functionality of semiconductor devices such as logic gates, latched circuits, and oscillators. This is followed with a review of the analysis, modeling, and simulation of natural and synthetic genetic circuits, which often proceed in a manner similar to that used for electronic systems. We conclude by presenting examples of naturally occurring genetic and biochemical systems that recently have been conceptualized in terms familiar to systems engineers. Our review of these newly forming fields of research demonstrates that the expertise and skills contained within electrical and computer engineering disciplines apply not only to design within biological systems, but also to the development of a deeper understanding of biological functionality. This review of these efforts points to the emergence of both engineering and basic science disciplines following parallel paths.