This book mainly focuses on basic concepts and model systems; but in reality, soft materials are complex and have a practical impact on our daily lives. These materials make up common products such as pharmaceutical formulations, paints, dairy products and cosmetics [1]. To connect the insights into depletion effects to practical applications, we highlight some of the unresolved questions and future directions that could be pursued.

The basic concept of the depletion interaction can explain many phenomena in practical systems (Chap. 1). It also quantifies several properties of model colloid–polymer mixtures and can qualitatively describe phenomena in applications. This also holds for depletion forces, which are well understood in simple model systems (Chap. 2); but the challenge ahead is to understand the interactions in mixtures in which the direct interactions between colloids and/or depletants are more realistic than pure hard-core interactions. Additionally, depletion forces are typically not pair-wise additive—certainly not in the case of relatively large depletants; hence, it is important to account for multi-body interactions. Measuring these multi-body forces, as well as interactions in more complex mixtures (such as those including charged colloids and/or polyelectrolytes), is still a major challenge. The establishment of an increasing number of advanced techniques is helpful here.

Phase diagrams summarise a material’s thermodynamic stability [2], quantifying the stable phase state(s) upon varying conditions [3]. For that reason, phase diagrams are crucial for materials design and/or process optimisation and constitute a major part of this book. It is clear that the size of the nonadsorbing polymers relative to the colloidal spheres plays a crucial role; this determines the phase diagram topology and the region over which such a mixture is stable. Theoretical approaches can describe the main equilibrium phase diagram of colloid–polymer mixtures [4] both qualitatively and semi-quantitatively [5] (Chaps. 3, 4). Nonequilibrium phenomena (e.g. aggregation, gelation and glass formation) also play an important role in dictating whether certain phase states are experimentally accessible (Chap. 4).

Colloidal gas–liquid interfaces have unique characteristics, including ultra-low interfacial tension and observable thermal capillary waves (Chap. 5). Although theory and experiment show reasonable agreement for the interfacial tension and thickness, model systems have so far been the main focus. The interfacial properties of mixtures with more complex interactions and/or shapes remain an open field for exploration. Fundamentally, this is of great interest as these parameters are tunable for colloidal suspensions, which is in contrast to molecular systems. From a practical point of view, these interfacial properties may be relevant for water-in-water emulsions, which can be composed of phase separating aqueous protein–polysaccharide mixtures. Stabilising the fluid–fluid interface of these emulsion droplets against coalescence requires intricate knowledge of the details of the interface and could be a promising method to develop fat/oil-free food emulsions and other compartmentalised aqueous structures.

In some cases, interactions between depletants are of importance, such as in binary colloidal systems (e.g. mixtures of small and large spheres, mixtures of spheres and rods). The presence of these depletant–depletant interactions significantly influences the phase behaviour (Chaps. 6, 7). For binary mixtures of hard spheres, the colloidal gas–liquid phase transition is absent, while solid–solid phase equilibria appear. Rods turn out to be highly efficient depletants; free volume theory predicts that they induce phase transitions at very low volume fractions, in line with computer simulations and experiments of well-defined systems.

Nematic, smectic and columnar liquid-crystalline phases can be induced by the addition of polymers to rods or platelets (Chaps. 8,9), and their phase behaviour turns out to be remarkably rich: a zoo of three-, four- and five-phase coexistence is found, although this may appear to be at odds with the Gibbs phase rule.

The addition of colloidal spheres to rod-like particles leads to interesting phase behaviour, such as a smectic phase consisting of alternating two-dimensional liquid-like layers of rods and spheres [6,7,8]. It not only demonstrates the possibility for control of colloidal self-assembly using depletion phenomena, but also highlights the clear need for the use of models to guide such efforts. Anisotropic mixtures display remarkable nonequilibrium phenomena, e.g. the formation of gels and glasses, and unconventional responses to shear forces [9, 10]; yet, these remain under-explored. The structure and dynamics of their phases have been studied using a range of experimental techniques, including X-ray and neutron scattering, microscopy and rheology; but further understanding of their properties is needed in order to capitalise on their potential applications.

The emergence of experimental model systems comprising cube-like colloids allows a new range of colloidal solids to be prepared. They show surprising structures depending on the exact shape and size of the cubes (Chap. 10). The parameter space (i.e. cube and polymer concentrations, cube shape and cube–polymer size ratio) of these mixtures is, however, almost impossible to fully explore experimentally. Therefore, the availability of a complete theoretical framework that successfully predicts the phase behaviour of cubes mixed with depletants is paramount for making scientific and technological progress. It must take the more complex solid phase states (e.g. \(\mathbb {C}_0\) -lattice and \(\mathbb {C}_1\) -lattice) in the theoretical descriptions into account. Further, the nonequilibrium behaviour of cubes and polymers remains yet unexplored.

Depletion interactions have also become relevant and/or recognised in fields beyond classic colloid science, such as biology and technology (Chap. 11). Depletion-induced phase separation can be used to concentrate or purify colloidal suspensions, and exploiting depletion insights in various separation and purification technology applications is still an open field.

Accurate prediction of the depletion forces between colloidal particles in crowded or confined spaces is another unresolved issue. Additionally, crowding phenomena in dense systems affect the dynamics. This is of relevance for understanding, for instance, the formation of structures [11] and the dynamics of proteins [12] in cells. Crowders and the related depletion effects can induce hierarchical assembly and mediate specific biomolecular interactions [13]. These are challenging and promising topics where chemistry, physics and biology and chemistry meet.

Photovoltaics [14], energy storage materials [15], emerging battery technologies, fuel cells and novel products often consist of multi-component colloids and/or colloid–polymer hybrid systems; and consequently, depletion phenomena play an important role as they provide structure, affect dynamics and modify the phase stability. The colloidal systems that underpin real-world examples are, however, much more complex than the relatively well-defined ones described in this book. It is crucial to extend this knowledge towards these complex systems.

Besides complexity due to shape, charge and crowding, the colloids used in a range of application areas are often soft (e.g. polymer brushes or surfactants), or attract one another due to Van der Waals and/or hydrophobic forces. Association colloids, such as surfactant or copolymeric micelles and vesicles, may drive depletion interactions but have hardly been explored. In practice, dispersity in size and surface chemistry is an issue with colloidal systems; and polymers may feature additional complexity by being, e.g. branched, multi-armed, comb-like, copolymeric, or even responsive to external stimuli, as is the case for some microgels and supramolecular polymers [16]. Predicting how these characteristics affect the physical properties of colloid–polymer mixtures is still difficult.

Another topic that has largely been neglected is the influence of depletion forces on the dynamic properties of multi-component colloidal mixtures. Without a doubt, the rheological properties have implications for the practical applications of these systems. The viscosity, for instance, is not just the result of the combined contributions of colloids and polymers of a colloid–polymer mixture; there must be a complex interplay [17] that also affects, for instance, the fluid-to-gel transition [18].

Despite the significant progress made in understanding the depletion interaction and resulting phase behaviour of colloidal systems, there is still a long way to go. With so many factors influencing the depletion interaction, it is almost impossible to explore them all experimentally; yet mastering their impact on the behaviour and properties is instrumental for the design of the next generation of soft materials. The application of theory and computer simulation to this challenge have significantly advanced our understanding; but there is still a need for more accurate and predictive models and advanced experimental and computer simulation tools that can take into account the various, more complex, factors that influence the depletion force and related properties in practice. Here, we also see opportunities for artificial intelligence and machine learning tools to be applied, which will undoubtedly accelerate the testing of concepts. This powerful combination of tools, and further interdisciplinary endeavours, will provide essential design rules for colloidal systems.

In summary, the depletion interaction is often employed as a tool to induce well-defined attractions in colloidal systems; but it is far more than that, profoundly impacting the phase behaviour and many other properties of colloidal dispersions. This makes it a fascinating and relevant field of research in its own right, with many fundamental questions still unanswered. Future research will, no doubt, lead to valuable insights into the behaviour of colloids, and lead to the development of new materials and technologies.