The number of publications on acoustic scene classification (ASC) in environmental audio recordings has constantly increased over the last few years. This was mainly stimulated by the annual Detection and Classification of Acoustic Scenes and Events (DCASE) competition with its first edition in 2013. All competitions so far involved one or multiple ASC tasks. With a focus on deep learning based ASC algorithms, this article summarizes and groups existing approaches for data preparation, i.e., feature representations, feature pre-processing, and data augmentation, and for data modeling, i.e., neural network architectures and learning paradigms. Finally, the paper discusses current algorithmic limitations and open challenges in order to preview possible future developments towards the real-life application of ASC systems.