Natural habitats of most living microorganisms are distinguished by a complex structure often formed by a porous medium such as soil. The dynamics and transport properties of motile microorganisms are strongly affected by crowded and locally anisotropic environments. Using Chlamydomonas reinhardtii as a model system, we explore the permeation of active colloids through a structured wall of obstacles by tracking microswimmers' trajectories and analyzing their statistical properties. Employing micro-labyrinths formed by cylindrical or elongated pillars, we demonstrate that the anisotropy of the pillar's form and orientation strongly affects the microswimmers' dynamics on different time scales. Furthermore, we discuss the kinetics of the microswimmer exchange between two compartments separated by an array of pillars. Quasi-2D PDMS-channels with arrays of pillars are used as a model system for a porous medium to study the effect of environmental anisotropy on the behavior of motile microalgae. The geometry of the surrounding gives rise to preferred swimming directions and affects the permeation probability. image