In this talk, we will present different types of input-output systems and some associated model order reduction methods arising from systems and control theory. First, we will focus on methods for linear time-invariant systems, in particular the Balanced Truncation and the Iterative Rational Krylov Algorithm. Next, we will discuss extensions to nonlinear, time-varying and/or parametric systems. In addition, we will show common numerical tasks appearing in the implementations of these methods.