  In this paper, we will show the blow-up of smooth solutions to the Cauchy
problem for the full compressible Navier-Stokes equations and isentropic
compressible Navier-Stokes equations with constant and degenerate viscosities
in arbitrary dimensions under some restrictions on the initial data. In
particular, the results hold true for the full compressible Euler equations and
isentropic compressible Euler equations and the blow-up time can be computed in
a more precise way. It is not required that the initial data has compact
support or contain vacuum in any finite regions. Moreover, a simplified and
unified proof on the blow-up results to the classical solutions of the full
compressible Navier-Stokes equations without heat conduction by Xin \cite{Xin}
and with heat conduction by Cho-Bin \cite{CJ} will be given.
