In this talk, the Cauchy problem for the 1D isentropic compressible Navier-Stokes equations is considered. When the viscosity depends on the density in a sublinear power law, we prove the global-in-time well-posedness of regular solutions with large data and far field vacuum. The key to the proof is the introduction of a well-designed reformulated structure by introducing some new variables and initial compatibility conditions, which, actually, can transfer the degeneracies of the time evolution and the viscosity to the possible singularity of some special source terms. Then, combined with the BD entropy estimates and transport properties of the so-called effective velocity, one can obtain the required uniform a priori estimates of corresponding solutions. It is worth pointing out that the well-posedness theory established here can be applied to the viscous Saint-Venant system for the motion of shallow water. This talk is based on a joint work with Dr. Hao Li (Fudan) and Dr. Shengguo Zhu (SJTU).