Learning from data streams is among the most vital fields of contemporary data mining. The online analysis of information coming from those potentially unbounded data sources allows for designing reactive up-to-date models capable of adjusting themselves to continuous flows of data. While a plethora of shallow methods have been proposed for simpler low-dimensional streaming problems, almost none of them addressed the issue of learning from complex contextual data, such as images or texts. The former is represented mainly by adaptive decision trees that have been proven to be very efficient in streaming scenarios. The latter has been predominantly addressed by offline deep learning. In this work, we attempt to bridge the gap between these two worlds and propose Adaptive Deep Forest (ADF) - a natural combination of the successful tree-based streaming classifiers with deep forest, which represents an interesting alternative idea for learning from contextual data. The conducted experiments show that the deep forest approach can be effectively transformed into an online algorithm, forming a model that outperforms all state-of-the-art shallow adaptive classifiers, especially for high-dimensional complex streams.