In the model of continuous distributed monitoring, a number of observers each see a stream of observations. Their goal is to work together to compute a function of the union of their observations. This can be as simple as counting the total number of observations, or more complex non-linear functions such as tracking the entropy of the induced distribution. Assuming that it is too costly to simply centralize all the observations, it becomes quite challenging to design solutions which provide a good approximation to the current answer, while bounding the communication cost of the observers, and their other resources such as their space usage. This survey introduces this model, and describe a selection results in this setting, from the simple counting problem to a variety of other functions that have been studied.
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