Containers, lids, and sleeve structures are disclosed. Particularly, sleeve structures configured for insulating, stabilizing, or both insulating and stabilizing a container are disclosed. Further, a sleeve structure including a plurality of circumferentially adjacent, longitudinally extending sections and a sleeve structure including one or more frustoconical regions are disclosed. Containers, lids, and sleeve structures including at least one stabilizing feature are disclosed. Assemblies including a lower container, associated lid and sleeve structure, wherein at least one of the lower container, the lid, or the sleeve structure includes at least one stabilizing feature for engaging at least a portion of a sleeve structure associated with an upper container, wherein the upper container is positioned longitudinally above and is substantially aligned or centered with respect to a lower container, are disclosed. Circumferentially separated stabilizing features, individually installable stabilizing features, integral stabilizing features, and removable stabilizing features are also disclosed.