In this talk, we address the global (in time) well-posedness of strong solutions to the three-dimensional isentropic compressible Navier-Stokes equations on general bounded domains subject to the general Navier slip boundary conditions with nonnegative initial density provided that the initial total mechanical energy is suitably small. Such solutions possess small energy but contain vacuum and may have large oscillations. This generalizes the corresponding theory of Huang-Li-Xin (Comm. Pure Appl. Math., 65 (2012), 549-585) for the Cauchy problem. The key step is to establish the uniform upper bound of the density, which is achieved by elaborate estimates on two kinds of commutators defined on bounded domains: one is a natural extension in the case of general bounded domains of the classic Riesz commutator and the other is that of the spatial derivatives with the solution mapping of the co-normal derivative problem of the Laplacian. The Lipschitz norm of the velocity, which is a base to the gradient estimates for the density, is achieved by exploiting a BMO type elliptic estimate for the gradient of the solutions to the Lame system subject to the general Navier slip boundary conditions.