Here, we review the design of optical cavities, transient and modulated responses, and theoretical models relevant to vibrational strong coupling (VSC). While planar Fabry-Perot cavities remain the most common choice for experiments involving vibrational polaritons, other choices including plasmonic and phononic nanostructures, extended lattice resonances, and wavelength-scale three-dimensionally confined dielectric cavities have unique advantages, which are discussed. Next, we review the nonlinear response to laser excitation of VSC systems revealed by transient pump-probe and 2DIR techniques. The assignment of various features observed in these experiments has been an important topic with significant recent progress and controversy. The modulation of VSC systems by various means such as ultrafast pulses and electrochemical methods is also described. Finally, theoretical approaches to understanding the physics and chemistry of VSC systems are reviewed with an eye toward their applicability and usefulness. These fall into two main categories: (1) solving for the eigenmodes of the system and (2) evolutionary techniques including the transfer-matrix method and its generalizations. The need for quantum optical methods of describing VSC systems is critically evaluated in light of current experimental work, and we discuss circumstances which necessitate consideration of the full in-plane dispersion of the Fabry-Perot cavities.