This paper introduces WILDCAT, a deep learning method which jointly aims at aligning image regions for gaining spatial invariance and learning strongly localized features. Our model is trained using only global image labels and is devoted to three main visual recognition tasks: image classification, weakly supervised pointwise object lo-calization and semantic segmentation. WILDCAT extends state-of-the-art Convolutional Neural Networks at three major levels: the use of Fully Convolutional Networks for maintaining spatial resolution, the explicit design in the network of local features related to different class modalities, and a new way to pool these features to provide a global image prediction required for weakly supervised training. Extensive experiments show that our model significantly out-performs the state-of-the-art methods.