According to the recent trend in data acquisition and processing technology, big data are increasingly available in the form of unbounded streams of elementary data items to be processed in real-time. In this paper we study in detail the paradigm of sliding windows, a well-known technique for approximated queries that update their results continuously as new fresh data arrive from the stream. In this work we focus on the relationship between the various existing sliding window semantics and the way the query processing is performed from the parallelism perspective. From this study two alternative parallel models are identified, each covering semantics with very precise properties. Each model is described in terms of its pros and cons, and parallel implementations in the FastFlow framework are analyzed by discussing the layout of the concurrent data structures used for the efficient windows representation in each model.