The neuronal networks of the olfactory system transduce and transform complex mixtures of odorant molecules into patterns of the neural activity representing smells. We explore two important aspects of how this process works, at the cellular and the neural circuit level, in modeling studies that produce experimental testable predictions. 1) It has long been known that (in rodents) initial synaptic olfactory processing occurs in the olfactory bulb (OB) glomeruli, but the roles of various juxtaglomerular neurons is still not well understood. Recent experimental studies indicate that endogenously bursting external tufted (ET) cells -- which connect olfactory receptor neurons (ORN; OB input) to mitral cells (MC; OB output) -- play a central role in coordinating intraglomerular activity. We develop a biophysically realistic, Hodgkin-Huxley-style ET cell model that includes membrane currents known to be essential for bursting. We use specialized smooth optimization methods to study the (local) sensitivity of its functional characteristics (e.g. burst duration, interburst interval) to parameters, and statistical analyses to characterize the (global) influence of different currents. 2) Odorant-evoked input to and output from the OB is temporally dynamic, and these dynamics are important in shaping odor perception. Inhalation-evoked input bursts of ORN activity occur with durations, latencies, and amplitudes that vary across glomeruli (for the same odorant) and also in individual glomeruli for different odorants, and similarly diverse activity patterns occur at the MC level. We investigate these dynamics using biophysical models of the ORN-MC and ORN-ET-MC circuits. The models’ inputs are taken from recordings of ORN calcium signals of head-fixed rats exposed to odorants and closely reproduce signals received by the real neurons. With this data-driven dynamical modeling approach, we are able to explore how the circuits’ response dynamics vary for different odorants, synaptic strengths, and intrinsic cellular parameters.