Brain rhythms are nearly always analyzed in the spectral domain in terms of their power, phase, and frequency. While this conventional approach has uncovered spike-field coupling, as well as correlations to normal behaviors and pathological states, emerging work has highlighted the physiological and behavioral importance of multiple novel oscillation features. Oscillatory bursts, for example, uniquely index a variety of cognitive states, and the nonsinusoidal shape of oscillations relate to physiological changes, including Parkinson's disease. Open questions remain regarding how bursts and nonsinusoidal features relate to circuit-level processes, and how they interrelate. By analyzing unit and local field recordings in the rodent hippocampus, we uncover a number of significant relationships between oscillatory bursts, nonsinusoidal waveforms, and local inhibitory and excitatory spiking patterns. Bursts of theta oscillations are surprisingly related to a decrease in pyramidal neuron synchrony, and have no detectable effect on firing sequences, despite significant increases in neuronal firing rates during periods of theta bursting. Theta burst duration is predicted by the asymmetries of its first cycle, and cycle asymmetries relate to firing rate, synchrony, and sequences of pyramidal neurons and interneurons. These results provide compelling physiological evidence that time-domain features, of both nonsinusoidal hippocampal theta waveform and the theta bursting state, reflects local circuit properties. These results point to the possibility of inferring circuit states from local field potential features in the hippocampus and perhaps other brain regions with other rhythms.