This review proposes to summarize the development of laser shock applications in a confined regime, mainly laser shock peening, over the past 50 years since its discovery. We especially focus on the relative importance of the source term, which is directly linked to plasma pressure. Discussions are conducted regarding the experimental setups, experimental results, models and numerical simulations. Confined plasmas are described and their specific properties are compared with those of well-known plasmas. Some comprehensive keys are provided to help understand the behavior of these confined plasmas during their interaction with laser light to reach very high pressures that are fundamental for laser shock applications. Breakdown phenomena, which limit pressure generation, are also presented and discussed. A historical review was conducted on experimental data, such as pressure, temperature, and density. Available experimental setups used to characterize the plasma pressure are also discussed, and improvements in metrology developed in recent years are presented. Furthermore, analytical and numerical models based on these experiments and their improvements, are also reviewed, and the case of aluminum alloys is studied through multiple works. Finally, this review outlines necessary future improvements that expected by the laser shock community to improve the estimation of the source term.