During tunneling, the tunnel face is required to be kept stable so as to avoid any major settlement or to prevent any fatal accidents due to collapse or blow out. In soft cohesive soils, collapse happen more often than tunneling in cohesionless soils. It becomes more difficult to assess the tunnel behavior when there is water bearing layers within the cover soil. Hence, during excavation, a suitable type of support mechanism, e.g., pressurized air, soil slurry, or earth pressure support, is generally mobilized in controlled manner to prevent any fatal face failure issues. In this paper, efforts have been made to critically review the currently available techniques for studying various tunnel stability models, which includes analytical, numerical and physical modeling. Accordingly, methods have been studied for calculating the minimum tunnel face pressure as described by the respective authors. The analytical approaches for estimating stability of the tunnel face are mainly grouped into Limit Equilibrium Method and Limit Analysis Method. While the former one is a static force equilibrium method, e.g., wedge-silo mechanism; the later one is a kinematic approach, based on bound theorems, involving development of kinematic admissible velocity field. Estimation using both the techniques, and their improvisation, like incorporating the phenomenon of reduction of the vertical load due to 3D soil arching effect, and thereby getting more realistic solutions has also been presented. Moreover, studies also indicate that numerical methods incorporating suitable advanced constitutive soil model can further improve the tunnel face stability analysis, which can also incorporate different bounding condition of soil as well as soil-structure interaction for 3D condition. On the other hand, a number of studies also highlights the ground/structural response due to tunnel construction, with relative study between the results obtained from various physical model tests, using centrifuge model or small-scale model. This paper provides a comparative study of different methods for estimating the safe tunnel face pressure, available in the literature, their pros and cons and thus their utilization for finding an integrated approach for future research works.