This paper deals with control systems consisting of linearly interconnected integrators (or delay lines) and scalar nonlinearities. For linear systems with saturating sensors, we mention results on observability and minimal realization. When saturations appear in actuators, questions of control become of interest, and we describe stabilization techniques. If there are feedback loops containing the nonlinearities, `recurrent neural nets' are obtained, and we discuss various issues relating to their computational power and identifiability of parameters. Parts of the work surveyed here were jointly pursued with Francesca Albertini, Renee Schwarzschild, Hava Siegelmann.