Data streams gained obvious attention by researches for years. Mining this type of data generates challenges because of their special nature. Classification is one of the major approaches of Data Stream Mining (DSM). Concept drift (changes in pattern of data over time) is one of the major challenges that is needed to be adapted in data streams. Another challenge is high dimensional data streams. This paper provides a review for classification techniques in adaptive data stream mining. Focusing on both challenges; concept drifts and dimensionality reduction and dividing these techniques into incremental and ensemble. Incremental classifiers such as Very Fast Decision Trees (VFDT) and Concept-adapting Very Fast Decision Trees (CVFDT) were tested. Adaptive Random Forests (ARF) was taken as an example for adaptive ensemble classifiers. Furthermore, a practical analysis between VFDT, CVFDT and ARF was held. The analysis was according to accuracy, processing speed, and tree size. Accuracy did not vary much between the three algorithms. ARF has much better results in speed and has the smallest number of tree nodes.