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Variational autoencoder (VAE) is a neural architecture that learns a deep latent variable model using an amortized variational inference model and has become a popular approach to generative modeling and high-dimensional data analysis. Structured VAEs extend vanilla VAEs by incorporating probabilistic graphical models to account for dependencies in the prior of latent variables that naturally extend VAEs to temporal modeling and sequential decision making. In this talk, I will present our recent efforts in developing structured VAEs for modeling high-dimensional temporal and spatio-temporal data as well as for high-dimensional Bayesian optimization. Our proposed models are defined either as Gaussian process prior VAEs or latent neural ODEs or PDEs. I will discuss these models and their robust and computationally efficient learning methods. I will also highlight some applications in longitudinal modeling of electronic health records and dynamical modeling of physical systems as well as single-cell data.