Hybrid systems refer to systems exhibiting mixed discrete-continuous behaviors and arise as a natural byproduct of the interaction of embedded processors with physical systems. In this talk, we focus on the verification of a class of properties of hybrid systems called stability. Stability captures the notion that small perturbations to the initial state or input to the system result in only small changes in the eventual behavior of the system. It is a fundamental requirement of any control system design. We present a first result on the decidability/undecidability boundary of stability verification of hybrid systems. Then, as a basis for developing approximation techniques, we present preorders between systems which preserve stability.