This review article focuses on the amplification and simulation of quantum light-matter interactions, particularly in the regimes of strong and ultrastrong coupling. The authors discuss the importance of these interactions in various fields of physics, including quantum optics, cavity quantum electrodynamics (QED), and optomechanics. They highlight the advantages of stronger quantum interactions, such as enhanced sensitivity in quantum measurements, faster dynamics, and increased system nonlinearities. The review covers methods for amplifying light-matter interactions, including classical and quantum drives, and explores the simulation of ultrastrong coupling using techniques like cavity-assisted Raman transitions, digital simulations, and variational methods. The article also discusses experimental demonstrations and theoretical proposals, emphasizing the potential of quantum simulations in overcoming the challenges of experimental control in ultrastrong coupling regimes. The review provides a comprehensive overview of the mechanisms and applications of amplifying and simulating quantum light-matter interactions, offering insights into the latest advancements and future directions in this field.This review article focuses on the amplification and simulation of quantum light-matter interactions, particularly in the regimes of strong and ultrastrong coupling. The authors discuss the importance of these interactions in various fields of physics, including quantum optics, cavity quantum electrodynamics (QED), and optomechanics. They highlight the advantages of stronger quantum interactions, such as enhanced sensitivity in quantum measurements, faster dynamics, and increased system nonlinearities. The review covers methods for amplifying light-matter interactions, including classical and quantum drives, and explores the simulation of ultrastrong coupling using techniques like cavity-assisted Raman transitions, digital simulations, and variational methods. The article also discusses experimental demonstrations and theoretical proposals, emphasizing the potential of quantum simulations in overcoming the challenges of experimental control in ultrastrong coupling regimes. The review provides a comprehensive overview of the mechanisms and applications of amplifying and simulating quantum light-matter interactions, offering insights into the latest advancements and future directions in this field.