  Let $\{{X}_k\}_{k\geq\mathbb{Z}}$ be a stationary sequence. Given $p\in(2,3]$
moments and a mild weak dependence condition, we show a Berry-Esseen theorem
with optimal rate $n^{p/2-1}$. For $p\geq4$, we also show a convergence rate of
$n^{1/2}$ in $\mathcal{L}^q$-norm, where $q\geq1$. Up to $\log n$ factors, we
also obtain nonuniform rates for any $p>2$. This leads to new optimal results
for many linear and nonlinear processes from the time series literature, but
also includes examples from dynamical system theory. The proofs are based on a
hybrid method of characteristic functions, coupling and conditioning arguments
and ideal metrics.
