In this review paper, we define and discuss the concept of complexity for heterogeneous systems. Due to the current progress in fabrication technology, modern micro-scale integrated systems may have a large number of interacting elements. Each of those elements not only displays its own dynamical properties, but also, in the most general case, can be nonlinear or can belong to different physical domains. We consider two different examples of systems that are complex in the terms we use in this paper. The first example is a network of oscillators and is heterogeneous since it is a mixed-signal system. The second example is an electrostatic vibration energy harvester, a micro scale system combining elements from the mechanical and electrical domains. In both cases we discuss the challenges that arise at the stage of the system design.