We present a new direction for increasing the interpretability of deep neural networks (DNNs) by promoting weight-input alignment during training. For this, we propose to replace the linear transformations in DNNs by our novel B-cos transformation. As we show, a sequence (network) of such transformations induces a single linear transformation that faithfully summarises the full model computations. Moreover, the B-cos transformation is designed such that the weights align with relevant signals during optimisation. As a result, those induced linear transformations become highly interpretable and highlight task-relevant features. Importantly, the B-cos transformation is designed to be compatible with existing architectures and we show that it can easily be integrated into virtually all of the latest state of the art models for computer vision - e.g. ResNets, DenseNets, ConvNext models, as well as Vision Transformers - by combining the B-cos-based explanations with normalisation and attention layers, all whilst maintaining similar accuracy on ImageNet. Finally, we show that the resulting explanations are of high visual quality and perform well under quantitative interpretability metrics.