In a world of global trading, maritime safety, security and efficiency are crucial issues. We propose a multi-task deep learning framework for vessel monitoring using Automatic Identification System (AIS) data streams. We combine recurrent neural networks with latent variable modeling and an embedding of AIS messages to a new representation space to jointly address key issues to be dealt with when considering AIS data streams: massive amount of streaming data, noisy data and irregular time-sampling. We demonstrate the relevance of the proposed deep learning framework on real AIS datasets for a three-task setting, namely trajectory reconstruction, anomaly detection and vessel type identification.