Biological systems make use of feedback in an extraordinary number of ways, on scales ranging from molecules to cells to organisms to ecosystems. In this talk I will discuss the use of concepts from control and dynamical systems in the analysis and design of biological feedback circuits at the molecular level. After a brief survey of relevant concepts from control theory and synthetic biology, I will present some recent results that combine modeling, identification, design and experimental implementation of biological feedback circuits. These results include the use of intrinsic noise for system identification in transcriptional regulatory networks, development of RNA-based, in vitro circuits for regulating the rates of transcription of two independent genetic sequences, and design of dynamics of for an in vivo oscillator using transcriptional delay. Using these results as examples, I will discuss some of the open problems and research challenges in the area of biomolecular feedback systems.