Synthetic biology aims to engineer biological systems to meet new challenges and teach us more about natural biological systems. These pursuits range from the building of relatively simple transcriptional circuits, to engineering the metabolism of an organism, to reconstructing entire genomes. While we are still emerging from the foundational stages of this new field, we are already using engineered cells to discover underlying biological mechanisms, develop new therapeutics, and produce natural products. In this dissertation, we discuss the application of synthetic biology principles to the development of memory and pulse-detecting genetic circuits. In Chapter 2, we use novel transcriptional positive-feedback based memory devices integrated in human cells to study heterogeneous responses to cellular stresses. We built doxycycline, hypoxia, and DNA damage sensing versions of the device, demonstrating its modularity. In Chapter 3, we discuss further applications of the memory device in the study of long-term responses to hypoxia, gamma radiation, and inflammation. Finally, in Chapter 4 we describe work leading to the future construction of a pulse-detecting genetic circuit integrated in the E. coli genome. The work presented here illustrates the general applicability of synthetic biology in the study of biological phenomena and brings us one step closer to achieving a more exquisite understanding and control of natural systems.