Biological systems are often studied under the most "physiological" conditions possible. However, purposeful perturbation of biological systems can provide much information about their dynamics, robustness, and function. Such perturbations are particularly easy to apply at the interface of molecular biophysics and cellular biology, at which complex and highly regulated networks emerge from the behavior of individual biomolecules. Due to the size of diffusion coefficients and the length scale of biomolecules, the fastest timescales at this interface extend to below a microsecond. Thus perturbations must be induced and detected rapidly. We focus on examples of proteins and RNAs interacting with themselves (folding) or one another (binding, signaling). Beginning with general principles that have been learned from simple models and perturbation experiments in vitro, we progress to more complex environments that mimic aspects of the living cell, and finally rapid perturbation experiments in living cells. On the experimental side we highlight in particular two classes of rapid perturbation methods (nanoseconds to seconds) that have been traditionally employed in biophysical chemistry, but that will become increasingly important in cell biology and in vivo: fast relaxation techniques and phase-sensitive modulation techniques. These techniques are now increasingly married with imaging to produce a spatiotemporal map of biomolecular stability, dynamics and, in the near future, interaction networks inside cells. Many important chemical processes occur on biologically fast timescales, and yet have important ramifications for slower biological networks.