  Over the past two decades, vibrational resonance has garnered significant
interest and evolved into a prominent research field. Classical vibrational
resonance examines the response of a nonlinear system excited by two signals: a
weak, slowly varying characteristic signal, and a fast-varying auxiliary
signal. The characteristic signal operates on a much longer time scale than the
auxiliary signal. Through the cooperation of the nonlinear system and these two
excitations, the faint input can be substantially amplified, showcasing the
constructive role of the fast-varying signal. Since its inception, vibrational
resonance has been extensively studied across various disciplines, including
physics, mathematics, biology, neuroscience, laser science, chemistry, and
engineering. Here, we delve into a detailed discussion of vibrational resonance
and the most recent advances, beginning with an introduction to characteristic
signals commonly used in its study. Furthermore, we compile numerous nonlinear
models where vibrational resonance has been observed to enhance readers'
understanding and provide a basis for comparison. Subsequently, we present the
metrics used to quantify vibrational resonance, as well as offer a theoretical
formulation. This encompasses the method of direct separation of motions,
linear and nonlinear vibrational resonance, re-scaled vibrational resonance,
ultrasensitive vibrational resonance, and the role of noise in vibrational
resonance. Later, we showcase two practical applications of vibrational
resonance: one in image processing and the other in fault diagnosis. This
presentation offers a comprehensive and versatile overview of vibrational
resonance, exploring various facets and highlighting promising avenues for
future research in both theory and engineering applications.
