Robust identification and tracking of the pupil provides key information that can be used in several applications such as controlling gaze-based HMIs (human machine interfaces), designing new diagnostic tools for brain diseases, improving driver safety, detecting drowsiness, performing cognitive research, among others. We propose a deep convolutional neural network for eye-tracking based on atrous convolutions and spatial pyramids. DeepEye is able to handle real world problems such as varying illumination, blurring and reflections. The proposed network was trained and evaluated on 94,000 images taken from 24 data sets recorded in real world scenarios. DeepEye outperforms previous eye-tracking methods tested with these data sets. It improves the results of the current state of the art in a 26%, achieving an accuracy of more than 70% in almost every data set in terms of percentage of pupils detected with a distance error lower than 5 pixels. DeepEye can be downloaded at: https://github.com/Fjaviervera/DeepEye.