Streaming data analysis potentially represents a significant shift in emphasis from schemes historically pursued for offline (batch) approaches to the classification task. In particular, a streaming data application implies that: (1) the data itself has no formal 'start' or 'end'; (2) the properties of the process generating the data are non-stationary, thus models that function correctly for some part(s) of a stream may be ineffective elsewhere; (3) constraints on the time to produce a response, potentially implying an anytime operational requirement; and (4) given the prohibitive cost of employing an oracle to label a stream, a finite labelling budget is necessary. The scope of this article is to provide a survey of developments for model building under streaming environments from the perspective of both evolutionary and non-evolutionary frameworks. In doing so, we bring attention to the challenges and opportunities that developing solutions to streaming data classification tasks are likely to face using evolutionary approaches.