Topologically Associating Domains (TADs) are fundamental structural and functional building blocks of human interphase chromosomes, yet mechanisms of TAD formation remain unknown. 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 can produce TADs as determined by our analyses of Hi-C data. Contrary to typical illustrations, each TAD consists of multiple dynamically formed loops, rather than a single static loop. Our model 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 depletion of CTCF versus cohesin. The emerging picture is that TADs arise from actively forming, growing, and dissociating loops, presenting a framework for understanding interphase chromosomal organization.