Compliant gas foil bearings are composed of two layers of thin metallic foil and a thin film of gas to support the journal. The bottom foil creates an elastic structure which supports the top foil. This support structure can take a variety of shapes that range from a series of bumps around the circumference to a series of overlapping leaves. The top foil and the rotation of the rotor create a wedge of air that supports the rotor. The complaint foil structure deforms in response to the pressure developed within the gas film. These bearings have several advantages over conventional fluid film bearings. These advantages include reduced weight due to the elimination of the oil system, stable operation at higher speeds and temperatures, low power loss at high speeds and long life with little maintenance. Some disadvantages of gas foil bearings are low load capacities at low speed and modest stiffness and damping values. Due to these properties, compliant gas foil bearings are commonly used in specialized applications such as compressors for aircraft pressurization, engines for turboshaft propulsion, air cycle machines (ACMs), turboexpanders, and small microturbines. The ability to predict the behavior of these bearings and design them to meet the needs of the application is invaluable to the design process. This behavior can include things such as bearing stiffness, damping, and load capacity. Currently most foil bearing analysis tools involve some sort of coupling between hydrodynamics and structural analyses. These analysis tools can often have convergence issues and can require the use of empirically derived characteristics. This paper reviews the current status of the compliant gas foil bearings research, focusing mainly on the journal bump-type gas foil bearings and the development of the analysis tools for these bearings. This paper contributes to the field by making recommendations of the future developments of the analytical tools of journal bump-type gas foil bearings.