Topologically associating domains (TADs) are fundamental structural and functional building blocks of human interphase chromosomes, yet the mechanisms of TAD formation remain unclear. Here, we propose that loop extrusion underlies TAD formation. In this process, cis-acting loop-extruding factors, likely cohesins, form progressively larger loops but stall at TAD boundaries due to interactions with boundary proteins, including CTCF. Using polymer simulations, we show that this model produces TADs and finer-scale features of Hi-C data. Each TAD emerges from multiple loops dynamically formed through extrusion, contrary to typical illustrations of single static loops. Loop extrusion both explains diverse experimental observations-including the preferential orientation of CTCF motifs, enrichments of architectural proteins at TAD boundaries, and boundary deletion experiments-and makes specific predictions for the depletion of CTCF versus cohesin. Finally, loop extrusion has potentially far-ranging consequences for processes such as enhancer-promoter interactions, orientation-specific chromosomal looping, and compaction of mitotic chromosomes.