  We consider multivariate $\mathbb{L}_2$-approximation in reproducing kernel
Hilbert spaces which are tensor products of weighted Walsh spaces and weighted
Korobov spaces. We study the minimal worst-case error
$e^{\mathbb{L}_2-\mathrm{app},\Lambda}(N,d)$ of all algorithms that use $N$
information evaluations from the class $\Lambda$ in the $d$-dimensional case.
The two classes $\Lambda$ considered in this paper are the class $\Lambda^{{\rm
all}}$ consisting of all linear functionals and the class $\Lambda^{{\rm std}}$
consisting only of function evaluations.
  The focus lies on the dependence of
$e^{\mathbb{L}_2-\mathrm{app},\Lambda}(N,d)$ on the dimension $d$. The main
results are conditions for weak, polynomial, and strong polynomial
tractability.
