Audio-driven facial animation is a rapidly evolving field that aims to generate realistic facial expressions and lip movements synchronized with a given audio input. This survey provides a comprehensive review of deep learning techniques applied to audio-driven facial animation, with a focus on both audio-driven facial image animation and audio-driven facial mesh animation. These approaches employ deep learning to map audio inputs directly onto 3D facial meshes or 2D images, enabling the creation of highly realistic and synchronized animations. This survey also explores evaluation metrics, available datasets, and the challenges that remain, such as disentangling lip synchronization and emotions, generalization across speakers, and dataset limitations. Lastly, we discuss future directions, including multi-modal integration, personalized models, and facial attribute modification in animations, all of which are critical for the continued development and application of this technology.