We survey some of our recent progress on the local well-posedness problem for compressible Navier-Stokes Equations with density dependent viscosity when initial density does not have a uniform positive lower bound.When viscosity coefficients are constant multiple of a power of density,we identify the class of initial data admitting a local classical solution local in time when the power is greater or equal t0 1.The questions on the singularity formation will also be addressed.This talk is mainly based on joint works with Y.Li,and R.Pan.