Reconfigurable, ordered matter offers great potential for future low-power computer memory by storing information in energetically stable configurations. Among these, skyrmions—which are topologically protected, robust excitations that have been demonstrated in chiral magnets1,2,3,4 and in liquid crystals5,6,7—are driving much excitement about potential spintronic applications8. These information-encoding structures topologically resemble field configurations in many other branches of physics and have a rich history9, although chiral condensed-matter systems so far have yielded realizations only of elementary full and fractional skyrmions. Here we describe stable, high-degree multi-skyrmion configurations where an arbitrary number of antiskyrmions are contained within a larger skyrmion. We call these structures skyrmion bags. We demonstrate them experimentally and numerically in liquid crystals and numerically in micromagnetic simulations either without or with magnetostatic effects. We find that skyrmion bags act like single skyrmions in pairwise interaction and under the influence of current in magnetic materials, and are thus an exciting proposition for topological magnetic storage and logic devices.