  This paper is dedicated to the global existence and optimal decay estimates
of strong solutions to the compressible viscoelastic flows in the whole space
$\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \&
Zhang and Hu \& Wang to the critical $L^p$ Besov space, which is not related to
the usual energy space. With aid of intrinsic properties of viscoelastic fluids
as in \cite{QZ1}, we consider a more complicated hyperbolic-parabolic system
than usual Navier-Stokes equations. We define "\emph{two effective
velocities}", which allows us to cancel out the coupling among the density, the
velocity and the deformation tensor. Consequently, the global existence of
strong solutions is constructed by using elementary energy approaches only.
Besides, the optimal time-decay estimates of strong solutions will be shown in
the general $L^p$ critical framework, which improves those decay results due to
Hu \& Wu such that initial velocity could be \textit{large highly oscillating}.
