The research of borehole stability that considers strata anisotropy has great significance for the development of unconventional oil and gas reservoir. In this paper, based on the systematic research both at home and abroad in the recent ten years, the overview of the main progress of this research was provided. The main anisotropy factors that affect the borehole stability include the regional stress size, the nature of regional stress, the difference of rock physical and mechanical parameters, well structure, hydration swelling, micro-cracks, and the angle of weak bedding plane. The influence mechanism of single parameter on the borehole stability and the strata stress system were introduced in detail. The strength of rock had the most importance on the borehole stability. For the strata that has weak bedding plane, the strength of rock has great difference in different direction of drilling. When drilling along the weak bedding plane, it is easy to cause hydration swelling, and the micro-cracks always develop, and in this condition, borehole is easy to be unstable. Therefore, the high inhibition drilling fluid system or oil-based drilling fluid should be used and at the same time the influence of weak bedding plane on the borehole stability should be studied. When drilling in complex strata, these single factors can not always exist alone, but co-exist. As a result, the couple research of each single factor on the influence of borehole stability has great significance in establishing reasonable countermeasures. With the deep understanding of complex geological characteristics of unconventional oil and gas reservoir, the enhancement of the study of basic theory, numerical simulation and near realtime dynamic simulation research based on 3D visual modeling of borehole stability that considers strata anisotropy is the main developing direction in the future.