Noise is an inherent part of neuronal dynamics, and thus of the brain. It can be observed in neuronal activity at different spatiotemporal scales, including in neuronal membrane potentials, local field potentials, electroencephalography, and magnetoencephalography. A central research topic in contemporary neuroscience is to elucidate the functional role of noise in neuronal information processing. Experimental studies have shown that a suitable level of noise may enhance the detection of weak neuronal signals by means of stochastic resonance. In response, theoretical research, based on the theory of stochastic processes, nonlinear dynamics, and statistical physics, has made great strides in elucidating the mechanism and the many benefits of stochastic resonance in neuronal systems. In this perspective, we review recent research dedicated to neuronal stochastic resonance in biophysical mathematical models. We also explore the regulation of neuronal stochastic resonance, and we outline important open questions and directions for future research. A deeper understanding of neuronal stochastic resonance may afford us new insights into the highly impressive information processing in the brain.