Improved inflatable packers are provided. A packer may be constructed from hybrid structures including slat structures and weave structures. A packer may include a bladder and a cover, with a plurality of slats disposed therebetween, and/or a weave structure or anti-extrusion layer disposed therebetween. The slats may vary in width and thickness, and be provided with a plurality of reinforcement members. The reinforcement members may be longitudinally and/or transversely disposed in the slats. One or more of the various components of the packer preferably include a fiber, a wire, a cable, a nanofiber, a nanotube, and/or a nanoparticle modified elastomer. Anchors may be attached to or embedded in the outer cover. The packer may include a carcass having an end coupling including a plurality of slats. Improved packer cups are also disclosed, and preferably include a body member reinforced with a nanotube or similar material.