State estimation is an essential part of intelligent navigation and mapping systems where tracking the location of a smartphone, car, robot, or a human-worn device is required. For autonomous systems such as micro aerial vehicles and self-driving cars, it is a prerequisite for control and motion planning. For AR/VR applications, it is the first step to image rendering. Visual-inertial odometry (VIO) is the de-facto standard algorithm for embedded platforms because it lends itself to lightweight sensors and processors, and maturity in research and industrial development. Various approaches have been proposed to achieve accurate real-time tracking, and numerous open-source software and datasets are available. However, errors and outliers are common due to the complexity of visual measurement processes and environmental changes, and in practice, estimation drift is inevitable. In this thesis, we introduce the concept of information deficiency in state estimation and how to utilize this concept to develop and improve VIO systems. We look into the information deficiencies in visual-inertial state estimation, which are often present and ignored, causing system failures and drift. In particular, we investigate three critical cases of information deficiency in visual-inertial odometry: low texture environment with limited computation, monocular visual odometry, and inertial odometry. We consider these systems under three specific application settings: a lightweight quadrotor platform in autonomous flight, driving scenarios, and AR/VR headset for pedestrians. We address the challenges in each application setting and explore how the tight fusion of deep learning and model-based VIO can improve the state-of-the-art system performance and compensate for the lack of information in real-time. We identify deep learning as a key technology in tackling the information deficiencies in state estimation. We argue that developing hybrid frameworks that leverage its advantage and enable supervision for performance guarantee provides the most accurate and robust solution to state estimation.