Structural maintenance of chromosomes (SMC) complexes organize the genome via DNA loop extrusion. Although some SMCs were reported to do so symmetrically, reeling DNA from both sides into the extruded DNA loop simultaneously, others perform loop extrusion asymmetrically toward one direction only. The mechanism underlying this variability remains unclear. Here, we examine the directionality of DNA loop extrusion by SMCs using in vitro single-molecule experiments. We find that cohesin and SMC5/6 do not reel in DNA from both sides, as reported before, but instead extrude DNA asymmetrically, although the direction can switch over time. Asymmetric DNA loop extrusion thus is the shared mechanism across all eukaryotic SMC complexes. For cohesin, direction switches strongly correlate with the turnover of the subunit NIPBL, during which DNA strand switching may occur. Apart from expanding by extrusion, loops frequently diffuse and shrink. The findings reveal that SMCs, surprisingly, can switch directions.