One of the key ideas in control theory is that of viewing a complex dynamical system as an interconnection of simpler subsystems, thus deriving conclusions regarding the complete system from the properties of its building blocks. Following this paradigm, and originally motivated by questions in cell signal transduction modeling, we recently developed with D. Angeli an approach based on components which are monotone systems with respect to partial orders in state and signal spaces and have well-defined steady-state characteristics. The talk will present a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback and on the emergence of multi-stability and associated hysteresis effects under positive feedback. We will also explain how one would apply these theorems in practical experimental situations, as discussed in our recent work with J. Ferrell.