Vehicle taillight recognition is an important application for automated driving, especially for intent prediction of ado vehicles and trajectory planning of the ego vehicle. In this work, we propose an end-to-end deep learning framework to recognize taillights, i.e. rear turn and brake signals, from a sequence of images. The proposed method starts with a Convolutional Neural Network (CNN) to extract spatial features, and then applies a Long Short-Term Memory network (LSTM) to learn temporal dependencies. Furthermore, we integrate attention models in both spatial and temporal domains, where the attention models learn to selectively focus on both spatial and temporal features. Our method is able to outperform the state of the art in terms of accuracy on the UC Merced Vehicle Rear Signal Dataset, demonstrating the effectiveness of attention models for vehicle taillight recognition.