Coupling internal and vibrational states of a string of trapped ions has proven to be an effective way of entangling the ions’ internal states. In recent experiments, we have used this mechanism for the demonstration of high-fidelity quantum gates, QND measurements of spin correlations and creation of large entangled states. However, these interactions are also of interest for the purpose of quantum simulations where the motional state no longer acts as an auxiallary quantum system only. In this talk, I will focus on an experiment where a laser-cooled trapped ion is set to behave as a free relativistic quantum particle. This experiment demonstrates that a system acting as a quantum simulator may have completely different physical properties than the quantum system to be simulated. In addition, I will also discuss quantum gate based approaches to quantum simulations and present recent experiments on small ion strings containing up to five ions.