Abstract: The human hand is a complex biological system able to perform numerous tasks with impressive accuracy and dexterity. Gestures furthermore play an important role in our daily interactions, and humans are particularly skilled at perceiving and interpreting detailed signals in communications. Creating believable hand motions for virtual characters is an important and challenging task. Many new methods have been proposed in the Computer Graphics community within the last years, and significant progress has been made towards creating convincing, detailed hand and finger motions. This state of the art report presents a review of the research in the area of hand and finger modeling and animation. Starting with the biological structure of the hand and its implications for how the hand moves, we discuss current methods in motion capturing hands, data-driven and physics-based algorithms to synthesize their motions, and techniques to make the appearance of the hand model surface more realistic. We then focus on areas in which detailed hand motions are crucial such as manipulation and communication. Our report concludes by describing emerging trends and applications for virtual hand animation.