Films like Shrek, Madagascar, The Chronicles of Narnia and Charlotte's web all have something in common: realistic quadruped animations. While the animation of animals has been popular for a long time, the technical challenges associated with creating highly realistic, computer generated creatures have been receiving increasing attention recently. The entertainment, education and medical industries have increased the demand for simulation of realistic animals in the computer graphics area. In order to achieve this, several challenges need to be overcome: gathering and processing data that embodies the natural motion of an animal - which is made more difficult by the fact that most animals cannot be easily motion-captured; build accurate kinematic models for animals, in particular with adapted animation skeletons; and develop either kinematic or physically-based animation methods, either embedding some a priori knowledge about the way that quadrupeds locomote and/or building on some example of real motion. In this state of the art report, we present an overview of the common techniques used to date for realistic quadruped animation. This includes an outline of the various ways that realistic quadruped motion can be achieved, through video-based acquisition, physics based models, inverse kinematics, or some combination of the above. The research presented represents a cross fertilisation of vision, graphics and interaction methods.