Vibrational resonance is a phenomenon where a weak, low-frequency signal is amplified by a high-frequency signal in a nonlinear system. This concept, first introduced by Landa and McClintock, has since been studied extensively across various fields, including physics, mathematics, biology, neuroscience, and engineering. The core elements of vibrational resonance include nonlinear systems, slowly varying characteristic signals, and fast varying auxiliary signals. The interaction of these elements allows for the amplification of weak signals, making vibrational resonance a valuable tool for signal detection and processing. The paper reviews the theoretical foundations of vibrational resonance, including the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, and ultrasensitive vibrational resonance. It also discusses the role of noise in vibrational resonance and presents various metrics used to quantify this phenomenon. The review highlights the importance of vibrational resonance in practical applications such as image processing and fault diagnosis. The paper also explores different types of excitations used in vibrational resonance, including periodic signals, aperiodic binary signals, frequency-modulated signals, amplitude-modulated signals, and logical signals. These excitations can induce various resonance patterns and are crucial for understanding the dynamics of nonlinear systems. Nonlinear models of vibrational resonance are classified into five main categories: ordinary differential systems, mapping systems, fractional differential systems, delayed differential systems, and stochastic differential systems. The paper presents several common nonlinear systems characterized by ordinary differential equation models, including symmetric and asymmetric bistable oscillators, monostable oscillators, quintic oscillators, periodic potential oscillators, and parametric oscillators. The review also discusses the effects of time delay, fractional-order systems, and noise on vibrational resonance. It highlights the importance of vibrational resonance in various engineering applications, such as energy harvesting and fault diagnosis. The paper concludes with a discussion of future research directions in the field of vibrational resonance.Vibrational resonance is a phenomenon where a weak, low-frequency signal is amplified by a high-frequency signal in a nonlinear system. This concept, first introduced by Landa and McClintock, has since been studied extensively across various fields, including physics, mathematics, biology, neuroscience, and engineering. The core elements of vibrational resonance include nonlinear systems, slowly varying characteristic signals, and fast varying auxiliary signals. The interaction of these elements allows for the amplification of weak signals, making vibrational resonance a valuable tool for signal detection and processing. The paper reviews the theoretical foundations of vibrational resonance, including the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, and ultrasensitive vibrational resonance. It also discusses the role of noise in vibrational resonance and presents various metrics used to quantify this phenomenon. The review highlights the importance of vibrational resonance in practical applications such as image processing and fault diagnosis. The paper also explores different types of excitations used in vibrational resonance, including periodic signals, aperiodic binary signals, frequency-modulated signals, amplitude-modulated signals, and logical signals. These excitations can induce various resonance patterns and are crucial for understanding the dynamics of nonlinear systems. Nonlinear models of vibrational resonance are classified into five main categories: ordinary differential systems, mapping systems, fractional differential systems, delayed differential systems, and stochastic differential systems. The paper presents several common nonlinear systems characterized by ordinary differential equation models, including symmetric and asymmetric bistable oscillators, monostable oscillators, quintic oscillators, periodic potential oscillators, and parametric oscillators. The review also discusses the effects of time delay, fractional-order systems, and noise on vibrational resonance. It highlights the importance of vibrational resonance in various engineering applications, such as energy harvesting and fault diagnosis. The paper concludes with a discussion of future research directions in the field of vibrational resonance.