The ability of a consistent marching scheme to reach a steady-state depends on its numerical as well as physical stability in a linear and time asymptotic sense. From this perspective, three different categories emerge based on the complex frequency associated with the linear gain. In the first one, the flow is physically stable. Hence, any consistent and numerically stable explicit marching scheme is capable of reaching a steady-state given an appropriate spatial discretization. This can be a challenge in high-speed flows due to compression fan and shock related temporal and spatial numerical oscillations. Recently developed WENO schemes can significantly minimize these issues. In the second category, the flow is physical unstable with a nonzero complex frequency. Most steady-state solvers in the literature were designed to deal with flows in this category. The recently developed multi-stage MGM schemes can provide the quadratic convergence of the Newton method without its sensitivity to initial conditions. Finally, the third category considers physically unstable flows with a zero complex frequency. Flows that are convectively unstable to stationary disturbances belong to this category. It turns out none of the existing steady-state solvers can prevent the spatial growth of these disturbances if steady numerical excitation sources cannot be removed. Some promising novel ideas capable of damping these disturbances are discussed.