A stent-valve for transcatheter implantation to replace a cardiac valve, the stent valve being compressible to a compressed state for delivery, and expandable to an operative state for implantation, the stent-valve comprising a stent, a plurality of leaflets for defining a prosthetic valve, an inner skirt, an outer skirt, and a paravalve seal for sealing against surrounding tissue. In some embodiments, the paravalve seal comprises material that swells in response to contact with blood. In some embodiments, the seal comprises a flap or pocket that is distensible in response to backpressure and/or paravalve back-flow of blood.