There is an important class of materials, many biological, that are highly porous and made by bonding rods, ribbons or fibres in both regular and irregular structures. These include paper, bone, wood, packaging foam and insulating fibre mats and they can be made of polymers, metals, ceramics and natural materials. Despite the different structures and materials, there are many similarities in how they behave. An important class of these materials is where the rods or ribbons form cells, co-called cellular structures. Here we explain how such structures deform in compression. To understand the deformation processes more easily the behaviour of a regular honeycomb structure is described before extending the ideas to structures such as foams.