An implantable prosthetic valve comprising: an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, the frame defining an axial direction extending from the inflow end to the outflow end; a leaflet structure positioned within the frame and secured thereto; and an annular outer skirt positioned around an outer surface of the frame, wherein the outer skirt comprises: an inflow edge portion secured to the frame at a first location; an outflow edge portion secured to the frame at a second location; an intermediate portion between the inflow edge portion and the outflow edge portion, wherein the intermediate portion comprises a plurality of circumferentially spaced, axially extending slits that define a plurality of skirt segments between each pair of slits, wherein each skirt segment comprises first and second opposing edge portions; wherein at least one of the first and second opposing edge portions of each of the plurality of skirt segments are secured to the frame and/or to other skirt segments so as to produce circumferential and/or twisting movement of the skirt segments upon radial expansion of the frame. an annular frame comprising an inflow end and an outflow end and being radially collapsible and expandable between a radially collapsed configuration and a radially expanded configuration, the frame defining an axial direction extending from the inflow end to the outflow end; a leaflet structure positioned within the frame and secured thereto; and an annular outer skirt positioned around an outer surface of the frame, wherein the outer skirt comprises: an inflow edge portion secured to the frame at a first location; an outflow edge portion secured to the frame at a second location; an intermediate portion between the inflow edge portion and the outflow edge portion, wherein the intermediate portion comprises a plurality of circumferentially spaced, axially extending slits that define a plurality of skirt segments between each pair of slits, wherein each skirt segment comprises first and second opposing edge portions; wherein at least one of the first and second opposing edge portions of each of the plurality of skirt segments are secured to the frame and/or to other skirt segments so as to produce circumferential and/or twisting movement of the skirt segments upon radial expansion of the frame. an inflow edge portion secured to the frame at a first location; an outflow edge portion secured to the frame at a second location; an intermediate portion between the inflow edge portion and the outflow edge portion, wherein the intermediate portion comprises a plurality of circumferentially spaced, axially extending slits that define a plurality of skirt segments between each pair of slits, wherein each skirt segment comprises first and second opposing edge portions; wherein at least one of the first and second opposing edge portions of each of the plurality of skirt segments are secured to the frame and/or to other skirt segments so as to produce circumferential and/or twisting movement of the skirt segments upon radial expansion of the frame.