Accurate duplication and separation of long linear genomic DNA molecules is associated with a number of purely mechanical problems. SMC complexes are key components of the cellular machinery that ensures decatenation of sister chromosomes and compaction of genomic DNA during division. Cohesin, one of the essential eukaryotic SMC complexes, has a typical ring structure with intersubunit pore through which DNA molecules can be threaded. Capacity of cohesin for such topological entrapment of DNA is crucial for the phenomenon of post-replicative association of sister chromatids better known as cohesion. Recently, it became apparent that cohesin and other SMC complexes are, in fact, motor proteins with a very peculiar movement pattern leading to formation of DNA loops. This specific process has been called loop extrusion. Extrusion underlies multiple functions of cohesin beyond cohesion, but molecular mechanism of the process remains a mystery. In this review, we summarized the data on molecular architecture of cohesin, effect of ATP hydrolysis cycle on this architecture, and known modes of cohesin-DNA interactions. Many of the seemingly disparate facts presented here will probably be incorporated in a unified mechanistic model of loop extrusion in the not-so-distant future.