  Strongly correlated layered 2D systems are of central importance in condensed
matter physics, but their numerical study is very challenging. Motivated by the
enormous successes of tensor networks for 1D and 2D systems, we develop an
efficient tensor network approach based on infinite projected entangled-pair
states (iPEPS) for layered 2D systems. Starting from an anisotropic 3D iPEPS
ansatz, we propose a contraction scheme in which the weakly-interacting layers
are effectively decoupled away from the center of the layers, such that they
can be efficiently contracted using 2D contraction methods while keeping the
center of the layers connected in order to capture the most relevant interlayer
correlations. We present benchmark data for the anisotropic 3D Heisenberg model
on a cubic lattice, which shows close agreement with quantum Monte Carlo (QMC)
and full 3D contraction results. Finally, we study the dimer to N\'eel phase
transition in the Shastry-Sutherland model with interlayer coupling, a
frustrated spin model which is out of reach of QMC due to the negative sign
problem.
