In this introductory talk I will discuss a theoretical framework suitable for the numerical study of confinement and the deconfinement transition. To this end I will introduce the basic notions of phase transitions and lattice gauge theory as well as associated Monte Carlo methods. Furthermore, I will present the classical picture of confinement and a novel approach based on clustering. In the end I will take a critical look at sample results.
The main goal of this talk is to give you an idea of how concepts of theoretical physics, numerical methods as well as concepts of computer science can join forces in order to shed light on a complex phenomenon observed in nature.