It is a well-known fact that apparently simple systems can give rise to complex behavior. But why exactly does a given system behave in a complex manner? There are two main approaches to tackle this and other related questions. One can take on a theoretical approach or else start from a more experimental study of the behavior of such systems with the help of a computer. In this paper, the experimental approach is applied to tag systems with a very small program size. After a discussion of some of the main theoretical results on tag systems, several results from a computer-assisted and experimental study on tag systems are analyzed. Special attention is given to the well-known example studied by Post with only 2 symbols and a deletion number v = 3. These results are combined with some theoretical results on tag systems in order to gain more insight into the computational power of simple tag systems.