**Abstract**
Simulating quantum systems is known to be a very difficult computational problem. In the early 1980s Richard Feynman suggested that only a quantum system would be able to efficiently simulate another quantum system. This observation led to the development of quantum information processing. Remarkable progress that has been made in this field, yet the original idea of a quantum simulator has not yet been put into practice although some attempts have been made. However, things are about to change due to the proposal by Porras and Cirac (/Phys. Rev. Lett/. *96*:250501 (2006)) for quantum simulation and computation with planar Coulomb crystals. This scheme is particularly promising because it makes use of the ion trap quantum computation technologies that at the moment are the most successful among the proposed systems for implementing quantum information processing.Motivated by the prospect of the experimental realization of applications like quantum simulation and scalable quantum computation, we have undertaken the task of investigating planar Coulomb crystals in detail. In this talk we will present the results we achieved so far and discuss the future prospects.