For a robot to interact with its environment, it must perceive the world and understand how the world evolves as a consequence of its actions. This thesis studies a few methods that a robot can use to respond to its observations, with a focus on instances that can leverage visual dynamic models. In general, these are models of how the visual observations of a robot evolves as a consequence of its actions. This could be in the form of predictive models that directly predict the future in the space of image pixels, in the space of visual features extracted from these images, or in the space of compact learned latent representations. The three instances that this thesis studies are in the context of visual servoing, visual planning, and representation learning for reinforcement learning. In the first case, we combine learned visual features with learning single-step predictive dynamics models and reinforcement learning to learn visual servoing mechanisms. In the second case, we use a deterministic multi-step video prediction model to achieve various manipulation tasks through visual planning. In addition, we show that conventional video prediction models are unequipped to model uncertainty and multiple futures, which could limit the planning capabilities of the robot. To address this, we propose a stochastic video prediction model that is trained with a combination of variational losses, adversarial losses, and perceptual losses, and show that this model can predict futures that are more realistic, diverse, and accurate. Unlike the first two cases, in which the dynamics model is used to make predictions for decision-making, the third case learns the model solely for representation learning. We learn a stochastic sequential latent variable model to learn a latent representation, and then use it as an intermediate representation for reinforcement learning. We show that this approach improves final performance and sample efficiency.