In recent years, the field of autonomous driving has attracted increasingly significant public interest. Accurately forecasting the future behavior of various traffic participants is essential for the decision-making of Autonomous Vehicles (AVs). In this paper, we focus on both scenario-based and perception-based motion forecasting for AVs. We propose a formal problem formulation for motion forecasting and summarize the main challenges confronting this area of research. We also detail representative datasets and evaluation metrics pertinent to this field. Furthermore, this study classifies recent research into two main categories: supervised learning and self-supervised learning, reflecting the evolving paradigms in both scenario-based and perception-based motion forecasting. In the context of supervised learning, we thoroughly examine and analyze each key element of the methodology. For self-supervised learning, we summarize commonly adopted techniques. The paper concludes and discusses potential research directions, aiming to propel progress in this vital area of AV technology.