In eukaryotes, genomic DNA is extruded into loops by cohesin¹. By restraining this process, the DNA-binding protein CCCTC-binding factor (CTCF) generates topologically associating domains (TADs)^2,3 that have important roles in gene regulation and recombination during development and disease^1,4–7. How CTCF establishes TAD boundaries and to what extent these are permeable to cohesin is unclear⁸. Here, to address these questions, we visualize interactions of single CTCF and cohesin molecules on DNA in vitro. We show that CTCF is sufficient to block diffusing cohesin, possibly reflecting how cohesive cohesin accumulates at TAD boundaries, and is also sufficient to block loop-extruding cohesin, reflecting how CTCF establishes TAD boundaries. CTCF functions asymmetrically, as predicted; however, CTCF is dependent on DNA tension. Moreover, CTCF regulates cohesin’s loop-extrusion activity by changing its direction and by inducing loop shrinkage. Our data indicate that CTCF is not, as previously assumed, simply a barrier to cohesin-mediated loop extrusion but is an active regulator of this process, whereby the permeability of TAD boundaries can be modulated by DNA tension. These results reveal mechanistic principles of how CTCF controls loop extrusion and genome architecture.