This project is aimed at providing a comprehensive analysis for stochastically driven hysteretic systems from various areas of science. While the quasi-static analysis of hysteretic systems has reached some degree of maturity, the stochastic and dynamic analysis is currently under major developments. Although the precise meaning of hysteresis might be different from one area to another, its origin is commonly due to the multiplicity of metastable states exhibited by that system. The physical systems are usually affected by internal or external noise, leading to a stochastic behavior of the system's output. The main objectives of this project are to develop methods for the stochastic analysis of hysteretic systems, to provide a comprehensive and unitary study of them, and to apply the results of this analysis in various areas of science and technology, such as magnetic data storage, photonic devices, shape-memory alloys, and computational neuroscience. The analysis and the control of the disruptive effects of noise in nonlinear systems with memory play a major role in the further development of the data storage technology. This project is expected to provide pertinent solutions to the current challenges related to the thermal stability of the recorded data and to help designing future memory devices. While it is mostly experienced as a disruptive effect, noise can also have a constructive role in hysteretic systems, activating a resonance response. Recent studies on nonlinear systems proved that such phenomena are quite common and their applications range from signal processing to climate models. This phenomenon is generally known as coherence resonance, when is solely induced by noise, and stochastic resonance, when an external oscillatory signal is present. Our analysis is also aimed at exploring the coherence and stochastic resonances in nonlinear systems with hysteresis and at deriving the rigorous conditions under which such resonance phenomena are possible.