A central problem in biology is to establish a relationship between the genotype of an organism and its phenotype. One part of this multi-scale problem is an understanding of the relationship between the structure of regulatory networks at the molecular level and the functioning of cells and cell aggregates. Mathematical systems biology approaches answers to these problems through the construction and analysis of mathematical models. A similar problem arises then for mathematical models of biological networks. What is the relationship between their structure and the resulting dynamics? This talk will explore this question in the context of algebraic models, that is, time-discrete dynamical systems over a finite state space. The talk is accessible to undergraduate students.