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Sequential recommender models are essential components of modern industrial recommender systems. These models learn to predict the next items a user is likely to interact with based on his/her interaction history on the platform. Most sequential recommenders however lack a higher-level understanding of user intents, which often drive user behaviors online. Intent modeling is thus critical for understanding users and optimizing long-term user experience. We propose a probabilistic modeling approach and formulate user intent as latent variables, which are inferred based on user behavior signals using variational autoencoders (VAE). The recommendation policy is then adjusted accordingly given the inferred user intent. We demonstrate the effectiveness of the latent user intent modeling via offline analyses as well as live experiments on a large-scale industrial recommendation platform.