Mining data streams in resource constrained environments has emerged as a challenging research issue for the data mining community in the past two years. Several approaches have been proposed to tackle the challenges of limited capabilities for small devices that generate or receive data streams. These approaches try to approximate the mining results with acceptable accuracy and efficiency in space and time complexity. However these approaches are not resource-aware. In this paper, a thorough discussion about the state of the art of mining data streams is presented followed by a formalization of our Algorithm Output Granularity (AOG) approach in mining data streams. The incorporation of AOG within a generic ubiquitous data mining system architecture is shown and discussed. The industrial applications of AOG-based mining techniques are given and discussed.