In the past two decades the physical and chemical properties of single-component metallic nanoparticles have been investigated very intensively [1,2,3]. The strong finite-size effects make computational approaches essential, especially in the small size regimes where properties depend non-trivially on the precise number of atoms. Larger nanoparticles in the scalable regime can also be described using mesoscopic approaches. Bringing two or more metals together leads to completely new phenomena, which do not have a counterpart in bulk materials [4,5]. For instance, several metals that are immiscible in the bulk can mix once at the nanoscale [6], sometimes into very unusual structures [7,8]. Nanoalloy particles show enhanced optical properties, which have already found applications in medicine as biosensors [9,10,11]. Once assembled in arrays, such systems could also provide media for optical data storage [12,13,14]. In this context, the strong magnetic anisotropy of some nanoalloy particles offers new perpectives in magnetic data storage [15,16]. Finally, the high surface-to-volume ratio of alloy nanoparticles also make them extremely appealing for heterogeneous catalysis [17,18].

The computational study of nanoalloys has expanded following several tracks. Since most physical properties are intimately related to the cluster geometry, a particular attention has been paid to structure prediction. The methods used for this purpose range from accurate ab initio calculations to empirical atomistic modelling and even mesoscopic approaches based on extrapolating finite-size behaviour. Global optimization of cluster structure is a formidable computational task, which can now be addressed using dedicated algorithms such as evolutionary-inspired methods or Monte Carlo schemes. Current applications concern systems containing up to hundreds of atoms when modelled with analytical force fields [19], up to a few tens of atoms if electronic structure is described explicitly [19,20]. The development of computer facilities and methodological improvements in density-functional theory have made modern electronic structure packages available, which allow systems containing up to several thousands atoms to be handled [21]. Besides the cluster geometry, electronic structure methods provide detailed information about the spectroscopic and optical properties [22]. However, for the purpose of studying dynamical or thermodynamical properties, atomistic potentials remain the only practical option. Most of such potentials are usually derived from well-known approximations to tight-binding theory [23,24] and can be improved using bond-order approaches [25,26]. These potentials are also usually parameterized on the basis of bulk properties and to a lesser extent surface properties, which may often be of concern when dealing with small size systems. Therefore, atomistic potentials deserve to be improved on the basis of electronic structure calculations.

Temperature has strong effects on the structure of alloy nanoparticles. It can alter the relative stability of specific structures, and induce geometric transitions [27]. For some elements, the degree of mixing or segregation depends on temperature and on the underlying structure [28,29]. Moreover, the melting process can be affected by changes in the composition of the particle. The mechanisms and kinetics of diffusion are two major issues governing the order-disorder transitions in these systems. At the present time, including the finite temperature effects is most often achieved through molecular dynamics or Monte Carlo simulations, sometimes involving Ising-model approximations [30]. 

The long-time dynamical processes involved in growth, coalescence, or slow diffusion are very difficult to investigate without severe approximations or even some coarse-graining. Explicit simulations are feasible only using analytical potentials. Some results have emphasized the role of kinetic effects in determining the stable structure of nanoalloy particles [31], particularly in the cases of segregated core-shell or onion-ring structures [32,33]. Bridging the time scale gap between molecular dynamics simulations and the experimentally relevant times requires the development of alternative approaches, such as accelerated molecular dynamics or kinetic Monte Carlo, which are already used for specific problems such as order-disorder transitions.

Another field where alloy nanoparticles offer unlimited possibilities is magnetism. In fact magnetic nanoalloys are likely to become as important to nanoscience as magnetic alloys are important to condensed matter and applied physics. The rapid development of this area is reflected by the number and quality of recent investigations [21,34,35]. All the central properties of a magnetic material (magnetization, magnetic anisotropy, and their temperature dependence) are most sensitive to alloying. Manipulating size and composition offers therefore remarkable perspectives, which eagerly call for the development of a consistent theoretical description. For example, one would like to grasp the microscopic mechanisms controlling the magnetic moments and magnetic anisotropy of 3d-4d and 3d-5d nanoalloys, since this would be extremely useful as a guide in the experimental development of nanoscale magnetic materials with optimized properties (e.g., nanoalloys with controlled anisotropy energies and moments for applications in recording media or spintronic devices). Thus, the potential impact of theoretical investigations is very high.

Understanding magnetic nanoalloys poses a major challenge for current numerical simulations. Besides the complexity of the many-body problem and relativistic effects that are inherent to magnetism in low symmetry nanostructures, one is here faced to the diversity of chemical configurations whose relative stability depends on the magnetic order and temperature. This concerns not only effects already observed in bulk magnetic alloys (e.g., hybridization effects between magnetic and non-magnetic elements) but also specific finite-size phenomena associated to the reduction of size, to changes in local coordination numbers, and to the interplay between surface, interface and bulk-like local environments. A successful progress in this direction (at the level of experimental expectations) requires coordinated efforts form experts on magnetism, statistical mechanics and multiscale modelling. 

Finally, it is important to observe that in most applications the alloy nanoparticles are not isolated as in the gas phase. For instance, ligand molecules are often attached at the surface of chemically synthesized nanoparticles in order to prevent them from reacting with the environment (e.g., solvent or biological tissues). Clusters from molecular beams are deposited at surfaces to form assembled materials, in which case the coupling with the support can be important. The interaction of the particle with these media can modify its properties, starting with the structure. Taking into account the presence of the surrounding media poses an additional complication to the computations, which has been successfully handled in several cases [36,37]. Further progress could be achieved by using hybrid quantum-mechanics/molecular-mechanics methods. Continuous descriptions of the substrate or solvent often offer a natural way of overcoming the length-scale gap.

There has already been a lot of efforts in tuning the optical properties of homogeneous metal nanoparticles for molecular diagnostics and use in bioconjugation or cellular labels, as well as DNA or protein markers for diseases [9,10,11]. Nanoalloys offer additional tunability, and gold-silver particles have recently been used for detecting DNA owing to a chip-based scanometric technique [38]. Even better detection thresholds have been reported by combining gold and magnetic nanoparticles [39]. Of course, coating nanoalloys is mandatory for any such biological application, which emphasizes the need for more investigations about their toxicity.

Many of the aforementioned problems could be certainly treated far more efficiently if the interplay between the various expertises were stronger. A better description of the electronic structure would have a significant impact on the quality of modelling, which in turn will allow more quantitative predictions of thermodynamic and kinetic properties. Progress in the sampling methods would directly affect the determination of structure and the study of phase transitions. Moreover, it would also help replacing trial-and-error schemes often unavoidable in electronic structure calculations. Efficient kinetic strategies for equilibrium and out-of-equilibrium problems would naturally benefit from explicit and accurate dynamical simulations. In sum, the development of integrated techniques and multi-scale modelling is crucial in order to reach quantitative predictions.