There is a wide class of phenomena which can be interpreted by using a dynamical system with a threshold as a model. Examples of these systems can be found in fields as diverse as digital communication and neurobiology. In this paper we discuss the dynamical behavior of threshold systems in the presence of noise. We show that both the dithering effect, well known to electronic engineers since the 1950s, and the phenomenon of stochastic resonance in threshold systems, recently introduced in the physical literature, can be described within the same scheme of noise activated processes. For these phenomena, in the absence of any frequency matching condition, the use of the term resonance is questionable and the notion of noice induced threshold crossings is more appropriate.
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