Spectroscopy of whispering-gallery mode microresonators has become a powerful scientific tool, enabling the detection of single viruses, nanoparticles and even single molecules. Yet the demonstrated timescale of these schemes has been limited so far to milliseconds or more. Here we introduce a scheme that is orders of magnitude faster, capable of capturing complete spectral snapshots at nanosecond timescales: cavity ring-up spectroscopy. Based on sharply rising detuned probe pulses, cavity ring-up spectroscopy combines the sensitivity of heterodyne measurements with the highest-possible, transform-limited acquisition rate. As a demonstration, we capture spectra of microtoroid resonators at time intervals as short as 16 ns, directly monitoring submicrosecond dynamics of their optomechanical vibrations, thermorefractive response and Kerr nonlinearity. Cavity ring-up spectroscopy holds promise for the study of fast biological processes such as enzyme kinetics, protein folding and light harvesting, with applications in other fields such as cavity quantum electrodynamics and pulsed optomechanics.