Cohesin organizes mammalian interphase chromosomes by reeling chromatin fibers into dynamic loops (Banigan and Mirny, 2020; Davidson et al., 2019; Kim et al., 2019; Yatskevich et al., 2019). "Loop extrusion" is obstructed when cohesin encounters a properly oriented CTCF protein (Busslinger et al., 2017; de Wit et al., 2015; Fudenberg et al., 2016; Nora et al., 2017; Sanborn et al., 2015; Wutz et al., 2017), and recent work indicates that other factors, such as the replicative helicase MCM (Dequeker et al., 2020), can also act as barriers to loop extrusion. It has been proposed that transcription relocalizes (Busslinger et al., 2017; Glynn et al., 2004; Lengronne et al., 2004) or interferes with cohesin (Heinz et al., 2018; Jeppsson et al., 2020; Valton et al., 2021; S. Zhang et al., 2021), and that active transcription start sites function as cohesin loading sites (Busslinger et al., 2017; Kagey et al., 2010; Zhu et al., 2021; Zuin et al., 2014), but how these effects, and transcription in general, shape chromatin is unknown. To determine whether transcription can modulate loop extrusion, we studied cells in which the primary extrusion barriers could be removed by CTCF depletion and cohesin's residence time and abundance on chromatin could be increased by Wapl knockout. We found evidence that transcription directly interacts with loop extrusion through a novel "moving barrier" mechanism, but not by loading cohesin at active promoters. Hi-C experiments showed intricate, cohesin-dependent genomic contact patterns near actively transcribed genes, and in CTCF-Wapl double knockout (DKO) cells (Busslinger et al., 2017), genomic contacts were enriched between sites of transcription-driven cohesin localization ("cohesin islands"). Similar patterns also emerged in polymer simulations in which transcribing RNA polymerases (RNAPs) acted as "moving barriers" by impeding, slowing, or pushing loop-extruding cohesins. The model predicts that cohesin does not load preferentially at promoters and instead accumulates at TSSs due to the barrier function of RNAPs. We tested this prediction by new ChIP-seq experiments, which revealed that the "cohesin loader" Nipbl (Ciosk et al., 2000) co-localizes with cohesin, but, unlike in previous reports (Busslinger et al., 2017; Kagey et al., 2010; Zhu et al., 2021; Zuin et al., 2014), Nipbl did not accumulate at active promoters. We propose that RNAP acts as a new type of barrier to loop extrusion that, unlike CTCF, is not stationary in its precise genomic position, but is itself dynamically translocating and relocalizes cohesin along DNA. In this way, loop extrusion could enable translocating RNAPs to maintain contacts with distal regulatory elements, allowing transcriptional activity to shape genomic functional organization.