Cellular structures are categorized according to their three-dimensional composition, regularity, and unit cell type. Planar cellular structures are generally referred to as honey-combs even if they do not contain the characteristic hexagonal pattern known from beehives. Three-dimensional structures characterized by a stochastic distribution of cell walls and sizes composed of open or closed polyhedra are categorized as foams. On the other hand, non-stochastic (i.e., regular, repeating) three-dimensional structures are classified as lattices. The smallest repeating entity of a lattice is the unit cell, which can be composed of struts or surfaces. Strut-based (also called graph-based) unit cells are categorized into bending-dominated and stretching-dominated types depending on their connectivity state at the corner nodes. Surface-based unit cells are divided into three-dimensional honeycombs and triply periodic minimal surface (TPMS) cells. TPMS lattices possess the useful property of dividing the occupied space into two separate volumes, rendering them especially suited for use as heat exchangers. Lattice structures behave much like expanded foam materials under compressive loads. Their performance during the compressive phase is strongly influenced by the relative density, \(\rho_{rel}=\rho^{*}/\rho_{s}\), where \(\rho^{*}\) is the apparent density of the cellular structure as determined by its external volume and total mass, and \(\rho_{s}\) is the density of the base material. A structure's porosity is, therefore, defined as \(1-\rho_{rel}\). Structures with a relative density of less than 30% are considered to be cellular, whereas they are considered to behave more like solids with isolated pores above this threshold [5]. In compression, foams exhibit an initially linear elastic regime wherein the response is governed by cell wall bending or stretching, depending on the cell morphology. The initial part of the stress-strain curve is the linear elastic phase; its derivative is defined as the apparent Young's modulus, \(E^{*}\). It is followed by a long collapse plateau at nearly constant (in the case of elastic-plastic materials) or slowly rising (in the case of elastomeric materials) stress until full densification is reached. Elastic-brittle materials cause a sharp stress decrease after the linear regime; the plateau is characterized by stress fluctuations caused by the successive brittle failure of the cells. Ductile materials show a smoother transition after the linear elastic regime with few or no fluctuations in the plateau phase. Both brittle and ductile material types may show successive layer collapses during the plateau phase, which is recognizable by its large, low-frequency force fluctuations. The long progression of the plateau phase permits large kinetic energy absorption potential that renders foams and lattice structures well suited for use as protection devices for sensitive electronics, wearable padding for sports purposes, etc. Lastly, densification is reached at the end of the plateau regime when opposing cell walls come into contact. The compressive response is then governed by the properties of the base material. Lattice structures share the described characteristics with foamed materials; however, the lattice's unit cell category can further influence their compressive response in different manners. Bending-dominated unit cell types (see Figure 1a) collapse early on because of the formation of compliant plastic hinges, causing a relatively smooth transition to the plateau regime (Figure 1b). On the other hand, stretching-dominated types yield later and more abruptly because of rupturing or buckling struts, causing a higher force peak at the end of the linear elastic regime and a sharp drop to the plateau regime stress level. The lattice categories are further subdivided into many different cell types such as the Simple Cubic (SC) cell, Face-Centred Cubic, Body-Centred Cubic, Fluorite, Diamond, Kelvin, Re-entrant, Weaire-Phelan, and combinations or alterations thereof.