This article presents a framework for understanding perception and prediction in the brain through the lens of hierarchical dynamical models and the free-energy principle. The authors propose that the brain operates as an inference engine, using a hierarchy of dynamical systems to model the world and infer the causes of sensory input. Perception is viewed as the optimization of these internal models to explain sensory data, with the free-energy principle providing a mathematical basis for this process. The paper outlines a general model of hierarchical dynamical systems, which can be used to simulate how the brain recognizes and predicts sensory sequences, such as birdsong. The authors demonstrate that the brain's anatomical and physiological structure is well-suited to implement this inference process, using synthetic models to illustrate how hierarchical models can be inverted to recover hidden states and causes from sensory data. The paper also explores the implications of these models for understanding brain function, including the role of hierarchical message passing, the importance of both structural and dynamical priors, and the ability of the brain to predict and categorize sensory input. The authors argue that the brain's hierarchical organization enables it to process complex sensory information and make predictions about future events, with the free-energy principle providing a unifying framework for understanding these processes. The paper concludes by emphasizing the importance of these models for understanding how the brain represents and predicts sensory information, and highlights the relevance of these ideas for both theoretical and applied neuroscience.This article presents a framework for understanding perception and prediction in the brain through the lens of hierarchical dynamical models and the free-energy principle. The authors propose that the brain operates as an inference engine, using a hierarchy of dynamical systems to model the world and infer the causes of sensory input. Perception is viewed as the optimization of these internal models to explain sensory data, with the free-energy principle providing a mathematical basis for this process. The paper outlines a general model of hierarchical dynamical systems, which can be used to simulate how the brain recognizes and predicts sensory sequences, such as birdsong. The authors demonstrate that the brain's anatomical and physiological structure is well-suited to implement this inference process, using synthetic models to illustrate how hierarchical models can be inverted to recover hidden states and causes from sensory data. The paper also explores the implications of these models for understanding brain function, including the role of hierarchical message passing, the importance of both structural and dynamical priors, and the ability of the brain to predict and categorize sensory input. The authors argue that the brain's hierarchical organization enables it to process complex sensory information and make predictions about future events, with the free-energy principle providing a unifying framework for understanding these processes. The paper concludes by emphasizing the importance of these models for understanding how the brain represents and predicts sensory information, and highlights the relevance of these ideas for both theoretical and applied neuroscience.