The paper reviews the phenomenon of stochastic resonance (SR), which occurs when the signal due to a weak periodic force in a nonlinear system is enhanced by the addition of external noise. The authors introduce a theoretical approach based on linear response theory (LRT), which is noted for its simplicity, generality, and predictive power despite being restricted to the small signal limit. The LRT approach is applied to overdamped motion in a bistable potential, the most common form of SR, and two new forms of SR predicted by LRT are described. These new forms include SR for fluctuational transitions between coexisting periodic attractors and for underdamped nonlinear oscillators in the absence of bistability. The paper also discusses the implications of these new forms of SR for various systems, such as passive optical systems, electron spin resonance, sensory neurons, and magneto-elastic strips. Experimental results from analogue electronic experiments are presented to validate the LRT predictions, demonstrating excellent agreement. The paper concludes by highlighting the value of LRT in understanding and predicting SR in a wide range of systems.The paper reviews the phenomenon of stochastic resonance (SR), which occurs when the signal due to a weak periodic force in a nonlinear system is enhanced by the addition of external noise. The authors introduce a theoretical approach based on linear response theory (LRT), which is noted for its simplicity, generality, and predictive power despite being restricted to the small signal limit. The LRT approach is applied to overdamped motion in a bistable potential, the most common form of SR, and two new forms of SR predicted by LRT are described. These new forms include SR for fluctuational transitions between coexisting periodic attractors and for underdamped nonlinear oscillators in the absence of bistability. The paper also discusses the implications of these new forms of SR for various systems, such as passive optical systems, electron spin resonance, sensory neurons, and magneto-elastic strips. Experimental results from analogue electronic experiments are presented to validate the LRT predictions, demonstrating excellent agreement. The paper concludes by highlighting the value of LRT in understanding and predicting SR in a wide range of systems.