Oxide materials have become high-tech functional materials beyond their traditional role as dielectrics. They show a rich variety of complex emergent behaviors, such as memristive effects, catalytic activity and complex multiferroic effects. At first glance ferroic effects, ionically driven modifications, and catalytic activity appear to play out in separate spheres: Ferroelectricity, ferromagentism, -elasticity and -toroidicity are properties of the ideal bulk material, ionics depend vitally on atomic scale defects, while catalytic activity is confined to surfaces. Consequently, the scientific exchange between the respective communities is limited. However, at closer examination ionics, ferroics, and catalytic activity are intimately linked. Grain boundaries, impurities and structural defects strongly influence the dynamics of  ferroic domains, catalytic activity often relies on atomic scale defects, such as oxygen vacancies, and can at the same time lead to the generation of new defects. At the same time the dynamics of defects are strongly influenced by local electric fields, domain boundaries, surfaces chemical potentials and other quantities influences by ferroic properties and catalytic action.

One of the most promising emerging technologies are memristors and the devices constructed from them. Memristors are passive two-terminal electronic devices which connect the magnetic flux φ to the charge q via a relationship of the form d φ = M(q,t)dq. The memristance M is a characteristic state function for the specific memristor. In the case of constant memristance the memristor is identical to an ohmic resistor M ≡ R. In the non-linear case I-V characteristics appear which otherwise can only be realized using active elements like transistors. This makes memristive devices technologically very interesting [1]. One particular application is the use of memristive devices as non-volatile memory. A simple, two-terminal passive element can be manufactured at much lower cost and much higher integration densities than active element based conventional memory cells. Even though the concept of memristive devices has already been developed in the 1970s from symmetry considerations of the basic equations of electronics [2], no physical manifestation could be realized for a long time. A specific class of memristors exhibits a hysteresis behavior which leads to at least two stable resistive states Ron ≪ Roff. These can be accessed by subjecting the devices to switching currents Iset < Ireset (where SET denotes the transition Roff → Ron and RESET the reverse). Technically, resistive switching elements have been realized as thin films of reduced oxides. A classification of models for resistive switching mechanisms is given in [3], based on the technical requirements on the resulting memory cells, redox-chemistry related mechanisms in oxides are of particularly high interest [3].
Very recent results show that nanoscale NbO cells exhibit an S-shaped I-V curve with negative differential resistance, which can be understood as locally active memristors exploiting a metal-insulator transition. These devices have been demonstrated to enable the construction of transistorless logic circuits and neuron emulation [4]. Especially, it is possible to replace the time-dependent resistors of the Hodgkin-Huxley model of neuronal action [5] with memristors, overcoming some of the model‘s limitations. Other theorized applications of memristors include transistorless differential amplifiers [6], adaptive filters [7] and programmable amplifiers [8]. At the current state of the art, the understanding of the ionic scale mechanisms governing the memristive effect in oxides is still rudimentary. Developing detailed, well understood theoretical models of these effects remains a major challenge.
More generally, conducting oxides are very promising materials for adaptive electronics applications [9]. Switching characteristics can not only be realized by nanionic effects leading to redox chemistry, but also by ferroelectric [10], ferromagnetic [11] or multiferroic materials [12]. Ferroelectrics display a hysteresis of the electrical polarizaton, characterized by a remanent polarization at zero electrical field and the possibility to continuously pole the material between positive and negative extrema. Fundamentally, the ferroelectric effect is well understood to be caused by an non-centrosymmetric distortion of the cystal leading to an emergent dipole moment [9]. Memristive I-V characterisics can be obtained from ferroelectric materials in various ways, including modulating the height of Schottky barriers between metal electrodes and a ferroelectric layer [20] or ferroelectric tunnel junctions where the tunnel barrier height across an ultrathin layer of ferroelectric materials is dependent upon the polarization direction [21]. Ferroelectrics offer not only possibilities for data storage, their applications encompass a wide variety of technical problems, such as magnetic field detection, or microwave, x-ray and neutron sources [13].
Resistive switching in ferromagnetic materials can be obtained by employing magnetic tunnel junctions [11] constructed from a thin insulating layer sandwiched between two ferromagnetic layers. The magnetization direction of one of these layers is pinned, while the other can be switched parallel or antiparallel to the first. In the parallel case only electrons of one spin state are strongly scattered, while in the antiparallel case, both electron spins are subject to scattering. Oxide-diluted magnetic semiconductors [14], such as Co:TiO2 thin films are highly interesting materials for spintronics, where there distribution and dynamics of the magnetic ions is of crucial importance for a detailed understanding of the materials properties. Dilute magnetic semiconductors offer attractive lab systems for fundamental physics [22], even though Curie temperatures well below room temperature so far preclude wide technical application. Current challenges include obtaining detailed theories how interfaces, surfaces and point defect influence the formation and propagation of ferroic domains.
Another highly important emerging technology based on oxides lies in advanced catalysis. The need to find sustainable methods of energy production leads to a demand for new methods of energy storage and distribution. While for ground transportation, storing electric energy from sustainable sources in batteries is demonstrated to be quite successful, this solution is out of the question for air travel. Here, chemical fuels for air-breathing engines may never be replaceable, due to their superior energy per weight ratio. At the current state of the art, the bulk of chemical fuels is produced by refining fossil hydrocarbons, i.e. Petrol. Most current technologies to produce chemical fuels from renewable biomass are extremely inefficient and therefore are neither economically viable nor do they offer ecological advantages [15]. Therefore, new methods to increase the energy density of biologically obtained hydrocarbons need to be developed.
Oxide catalysts have for long been used in oxidation catalysis and especially reducible oxides display high activity also at low temperatures. Therefore, oxide catalysts have been important in the development of efficient air cleaning systems operative at room temperature and been considered for the potential application in fuel cells, where low temperatures are required. Interestingly, while the catalytic activity of these compounds have been known for long, recent experiments for the reducible oxides of cobalt [23] and cerium [24] have shown a large dependency of the catalytic activity with the nature of the oxide catalyst in terms of size and morphology. Furthermore, the catalytic activity of oxides can be strongly influenced by surface and subsurface point defects [18], while the ongoing reaction can strongly influence the distribution of point defects on and within the oxide catalyst itself [19]. Oxide catalysts may allow better control over the reaction products than conventional noble metal catalysts through defect level engineering [16] and are therefore a promising route towards the development of more efficient catalysts. One exciting example of novel oxide catalysts is nanoscale gold oxide centers [17].
Besides being catalytically active, oxide materials are often used in conjunction with catalytically active metals as catalytic promoters. For example, in the case of automotive catalysis using the three-way catalyst, ceria (CeO2) has for long been used as oxygen buffer to provide oxygen at reducing conditions [25]. Interestingly, as with the catalytic activity, a size dependent effect on the oxygen transfer from the oxide compound to the catalytically active metal particles has been observed [26]. While in this case, the role of the promoting oxide is clear; this is not always the case. In industrial catalysis, it is well known that synergetic effects between catalytically active metals and metal oxide compounds are important for the overall efficiency. Most often, the role of the catalytically active metal is well known, but the actual role of the promoting oxide compound is far less understood. Recently, a combined experimental and theoretical study have elucidated the role of ZnO in methanol synthesis over Cu based industrial catalysts [27]. In contrast to most studies where ZnO is considered as a as support for Cu nano-particles, it was shown that the role of ZnO is to provide active sites through Zn atoms decorating steps on the Cu metal particle [27]. This example illustrates the complexity when it comes to understanding the role of oxides in heterogeneous catalysis which depend crucially on the nature of the oxide compound in terms of size, morphology, stoichiometry and possible defects. A detailed understanding of possible synergetic effects is identified as a key challenge when it comes to develop new more efficient catalytic concepts.