During the last decade, considerable effort has been made to perform automatic classification of variable stars using machine-learning techniques. Traditionally, light curves are represented as a vector of descriptors or features used as input for many algorithms. Some features are computationally expensive, cannot be updated quickly and hence for large data sets such as the LSST cannot be applied. Previous work has been done to develop alternative unsupervised feature extraction algorithms for light curves, but the cost of doing so still remains high. In this work, we propose an end-to-end algorithm that automatically learns the representation of light curves that allows an accurate automatic classification. We study a series of deep learning architectures based on recurrent neural networks and test them in automated classification scenarios. Our method uses minimal data pre-processing, can be updated with a low computational cost for new observations and light curves, and can scale up to massive data sets. We transform each light curve into an input matrix representation whose elements are the differences in time and magnitude, and the outputs are classification probabilities. We test our method in three surveys: OGLE-III, Gaia, and WISE. We obtain accuracies of about in the main classes and in the majority of subclasses. We compare our results with the Random Forest classifier and obtain competitive accuracies while being faster and scalable. The analysis shows that the computational complexity of our approach grows up linearly with the light-curve size, while the traditional approach cost grows as Nlog (N).