Abstract: In the space plasma environments, there are a variety of electromagnetic structures, including current sheets, magnetic holes and flux ropes, for which scales range from fluid down to ion or even electron kinetic scales. Our understanding of these structures, especially their electromagnetic field profiles and particle distributions, has been greatly improved due to the recent improvement in spacecraft technologies and enhancement in the observational database. To fully achieve the three-dimensional configurations of these structures, it is insufficient to use only the observations but also the theoretical models and numerical simulations. This paper briefly reviews the general framework of constructing theoretical models over these structures, which are self-consistent equilibrium solutions of Vlasov-Maxwell equations. In this framework, to ensure the satisfaction of the equilibrium Vlasov equation, particle distribution is expressed as a function of the particle invariant's motion. The moments of the particle distributions are then substituted into the Maxwell equations to solve the profiles of electromagnetic fields, which are further used to determine the particle phase space densities that can be compared directly to spacecraft observations. In recent years, this framework has been widely applied in the modeling and reconstruction of electromagnetic structures, demonstrating the ubiquitous presence of kinetic equilibrium structures in space plasmas. Moreover, the self-consistent models can be used as initial conditions of kinetic simulations. Finally, we discuss the open questions and future directions in studying kinetic structures in space plasmas.