The cornerstone of our understanding of nucleation lies in classical nucleation theory. This theory does an excellent job of showing why nucleation is an activated process, and why it typically occurs at a surface. However, in particular for nucleation at surfaces it can be highly inaccurate or even qualitatively wrong [1,2]. This problem can be overcome via computations using specialised algorithms for the study of activated processes. Computational algorithms such as umbrella sampling [3,4], and recent developments such as forward-flux sampling (FFS)  can calculate nucleation rates exactly and relatively efficiently. However even FFS cannot calculate rates in the presence of slow dynamics  (as found for example in glasses and gels). Modern sophisticated algorithms for dealing with the rough energy landscapes are available but have not yet been applied to crystallisation. Examples that we believe are particularly relevant to nucleation are the methods for locating local minima, their connectivity and transition states that have been pioneered by Wales and coworkers , and methods that have been developed for activated processes such as the "string" method .
The only experimental systems in which we have the techniques to study the microscopic details of crystallisation are model colloidal dispersions [9,10,11], where the interactions can also be carefully controlled. Model experimental systems have progressed beyond hard spheres to include: mixtures of oppositely charged ionic particles ; colloid-polymer mixtures  the study of field-induced martensitic phase transitions between exotic crystal structures ; controlled frustration due to impurities  and the competition between crystallization and vitrification . Moving to somewhat more complex situations, sedimentation can compete with crystallization  or be controlled : colloidal epitaxy , in fact experiments in microgravity showed a novel dendritic growth morphology, suggesting that even weak gravitational fields may play an important role in influencing the mechanism of crystal growth .
Like the experiments on model systems, recent simulation work has also moved beyond simple one-step homogeneous nucleation to look at more complex systems. For example, systems with multi-step nucleation , poisoning , and competing polymorphs . All these studies are for simple models of colloids or of simple molecules (e.g., noble gases).
So, we are studying more complex systems in both simulation and colloid experiments. However, even in colloids we are only starting to understand complex phenomena such as poisoning and in more complex molecular systems our understanding is much less developed.
The time is now right, and we have many of the tools required, to model and hence try to understand systems that are quite complex but are key to, for example, large industries and biological processes. An example is calcium carbonate which is important both inapplications such as the paper industry, and in which we wish to understand the many examples of its controlled mineralisation in biology  (biomineralisation). Recent experimental work [24,25] on this system has found small long-lived nanoclusters that appear to be precursors to crystallization. It appears that crystallization in this highly important system is very different from the classical picture, but there have not yet been simulations of this phenomenon. By contrast simulation of crystal growth during chemical vapour deposition as identified the importance of molecular pathways in controlling the growth rate .
Other outstanding problems include the two-step nucleation process of the protein haemoglobin the microscopic phenomenon that underlies sickle-cell anaemia  and the anti-AIDS drug Ritonavir . Ritonavir, like almost all substances, has several polymorphs. A highly stable second polymorph appeared during production of the drug and caused an estimated $250 million of losses due to lost production. The second polymorph appeared only after full-scale production had begun because nucleation of this form is extremely slow.