We recently used in situ Hi-C to create kilobase-resolution 3D maps of mammalian 
genomes. Here, we combine these maps with new Hi-C, microscopy, and 
genome-editing experiments to study the physical structure of chromatin fibers, 
domains, and loops. We find that the observed contact domains are inconsistent 
with the equilibrium state for an ordinary condensed polymer. Combining Hi-C 
data and novel mathematical theorems, we show that contact domains are also not 
consistent with a fractal globule. Instead, we use physical simulations to study 
two models of genome folding. In one, intermonomer attraction during polymer 
condensation leads to formation of an anisotropic "tension globule." In the 
other, CCCTC-binding factor (CTCF) and cohesin act together to extrude unknotted 
loops during interphase. Both models are consistent with the observed contact 
domains and with the observation that contact domains tend to form inside loops. 
However, the extrusion model explains a far wider array of observations, such as 
why loops tend not to overlap and why the CTCF-binding motifs at pairs of loop 
anchors lie in the convergent orientation. Finally, we perform 13 genome-editing 
experiments examining the effect of altering CTCF-binding sites on chromatin 
folding. The convergent rule correctly predicts the affected loops in every 
case. Moreover, the extrusion model accurately predicts in silico the 3D maps 
resulting from each experiment using only the location of CTCF-binding sites in 
the WT. Thus, we show that it is possible to disrupt, restore, and move loops 
and domains using targeted mutations as small as a single base pair.