Difference algebraic groups, i.e., groups defined by algebraic difference equations occur naturally as the Galois groups of linear differential or difference equations depending on a discrete parameter. The talk will start with a brief introduction to difference algebra and difference algebraic geometry. Then I will present some basic results on difference algebraic groups. In particular, I will introduce some numerical invariants, such as the limit degree, and discuss two possible definitions of the identity component of a difference algebraic group. Finally, I will explain the role of these concepts in a decomposition theorem for étale difference algebraic groups.