Pollution of the marine environment by large and microscopic plastic fragments and their potential impacts on organisms has stimulated considerable research interest and has received widespread publicity. However, relatively little attention has been paid to the fate and effects of microplastic particles that are fibrous in shape, also referred as microfibres, which are mostly shed from synthetic textiles during production or washing. Here we assess composition and abundance of microfibres in seafloor sediments in southern European seas, filling gaps in the limited understanding of the long-range transport and magnitude of this type of microplastic pollution. We report abundances of 10-70 microfibres in 50 ml of sediment, including both natural and regenerated cellulose, and synthetic plastic (polyester, acrylic, polyamide, polyethylene, and polypropylene) fibres. Following a shelf-slope-deep basin continuum approach, based on the relative abundance of fibres it would appear that coastal seas retain around 33% of the sea floor microfibres, but greater quantities of the fibres are exported to the open sea, where they accumulate in sediments. Submarine canyons act as preferential conduits for downslope transport of microfibres, with 29% of the seafloor microfibres compared to 18% found on the open slope. Around 20% of the microfibres found had accumulated in the deep open sea beyond 2000m of water depth. The remoteness of the deep sea does not prevent the accumulation of microfibres, being available to become integrated into deep sea organisms.