"Digital human characters are a mainstay of video games, film, and interactive computer graphics applications. However, animating hands remains a challenging aspect of human character animation: posing the hand involves coordinating many degrees of freedom, synthesizing a plausible grasp requires careful placement of contacts, and realistic rendering must account for intricate colour and texture variations. Traditional solutions to these problems require significant manual effort by skilled artists. It is therefore of great interest to computer animation researchers to develop fast and automatic methods for animating hands. This thesis presents methods for improving the realism of hands in real-time physics-based virtual environments.We begin by presenting a framework for skilled motion synthesis, wherein reinforcement learning and non-linear continuous optimization are used to generate controllers for single-handed re-orientation tasks. A mid-level multiphase approach breaks the problem into three parts, providing an appropriate control strategy for each phase and resulting in cyclic finger motions that accomplish the task. The exact trajectory is never specified, as the task goals are concerned with the final orientation and position of the object. Offline simulations are used to learn controller parameters, but the resulting control policy is suitable for real-time applications.We then describe a method for the simulation of compliant articulated structures using an approximate model that focuses on plausible endpoint behaviour. The approach is suitable for simulating physics-based characters under static proportional derivative control and stiff kinematic structures, like robotic grippers. The computation time of the dynamical simulation is reduced by an order of magnitude, and faster than real-time frame rates are easily achieved. Additionally, the state of internal bodies is computed independently, and in a parallel fashion.We also demonstrate an approach for synthesizing colour variation in fingers due to physical interaction with objects. A data-driven model relates contact information to visible colour changes for the fingernail and surrounding tissue on the back of the fingertip. The model construction uses the space of hemoglobin concentrations, as opposed to an RGB colour space, which permits transferability across different fingers and different people. Principal component analysis (PCA) on the sample images results in a compact model, enabling efficient implementation as a fragment shader program.Finally, we introduce a system for capturing grasping and dexterous interactions with real-world objects. A novel sensor ensemble collects information about joint motion and pressure distributions for the hand, and the data is used to design grasping controllers for a physics-based climbing simulation. Additionally, we speculate on how the interaction data can be used to derive future control strategies in physics-based animation. Combining interaction data with physical models is a promising approach for skilled motion synthesis involving hands." --