  In this paper we consider $L_p$-approximation, $p \in \{2,\infty\}$, of
periodic functions from weighted Korobov spaces. In particular, we discuss
tractability properties of such problems, which means that we aim to relate the
dependence of the information complexity on the error demand $\varepsilon$ and
the dimension $d$ to the decay rate of the weight sequence $(\gamma_j)_{j \ge
1}$ assigned to the Korobov space. Some results have been well known since the
beginning of this millennium, others have been proven quite recently. We give a
survey of these findings and will add some new results on the
$L_\infty$-approximation problem. To conclude, we give a concise overview of
results and collect a number of interesting open problems.
