Empty spaces are abhorred by nature, which immediately rushes in to fill the void. Humans have learnt pretty well how to make ordered empty nanocontainers, and to get useful products out of them. When such an order is imparted to molecules, new properties may appear, often yielding advanced applications. This review illustrates how the organized void space inherently present in various materials: zeolites, clathrates, mesoporous silica/organosilica, and metal organic frameworks (MOF), for example, can be exploited to create confined, organized, and self-assembled supramolecular structures of low dimensionality. Features of the confining matrices relevant to organization are presented with special focus on molecular-level aspects. Selected examples of confined supramolecular assemblies - from small molecules to quantum dots or luminescent species - are aimed to show the complexity and potential of this approach. Natural confinement (minerals) and hyperconfinement (high pressure) provide further opportunities to understand and master the atomistic-level interactions governing supramolecular organization under nanospace restrictions.