Synthetic biology may be viewed as an effort to establish, formalize, and develop an engineering discipline in the context of biological systems. The ability to tune the properties of individual components is central to the process of system design in all fields of engineering, and synthetic biology is no exception. A large and growing number of approaches have been developed for tuning the responses of cellular systems, and here we address specifically the issue of tuning the rate of response of a system: given a system where an input affects the rate of change of an output, how can the shape of the response curve be altered experimentally? This affects a system's dynamics as well as its steady-state properties, both of which are critical in the design of systems in synthetic biology, particularly those with multiple components. We begin by reviewing a mathematical formulation that captures a broad class of biological response curves and use this to define a standard set of varieties of tuning: vertical shifting, horizontal scaling, and the like. We then survey the experimental literature, classifying the results into our defined categories, and organizing them by regulatory level: transcriptional, post-transcriptional, and post-translational.