Oscillations are a prevalent feature of brain recordings. They are believed to play key roles in neural communication and computation. Current analysis methods for studying neural oscillations often implicitly assume that the oscillations are sinusoidal. While these approaches have proven fruitful, we show here that there are numerous instances in which neural oscillations are nonsinusoidal. We highlight approaches to characterize nonsinusoidal features and account for them in traditional spectral analysis. Instead of being a nuisance, we discuss how these nonsinusoidal features may provide crucial and so far overlooked physiological information related to neural communication, computation, and cognition.