This paper offers an extensive review of publications dealing with the modeling, the design and the experimental investigation of grooved dynamic gas lubricated bearings. Recent years have witnessed a rise in small-scale and high-speed turbomachinery applications. Besides the well-known gas foil bearings, grooved bearings offer attractive advantages, which unveil their potential in particular at small scale due to the structural simplicity as well as satisfying predictability. This paper starts with a general background of the application of gas lubricated bearings and introduces and compares the different gas bearing topologies. Further, the state-of-the-art modeling of grooved gas lubricated bearings is introduced in a systematic way assessing the advantages and inconveniences of two major approaches, the Narrow Groove Theory (NGT) and direct discretization method. Since NGT method is an elegant and efficient approach to model the complex effects of periodic grooves, a critical section is dedicated to the Narrow Groove Theory. In a second phase different models to include additional physical phenomena such as real gas lubrication, rarefaction or turbulence effects are reviewed. The paper concludes with a critical assessment of the state-of-the-art and indicates potential fields of research that would allow to shed more light into the understanding of these bearings, as well as with some thoughts on the integrated design methodologies of gas bearing supported rotors.