Traditional recommender systems primarily rely on a single type of user-item interaction, such as item purchases or ratings, to predict user preferences. However, in real-world scenarios, users engage in a variety of behaviors, such as clicking on items or adding them to carts, offering richer insights into their interests. Multi-behavior recommender systems leverage these diverse interactions to enhance recommendation quality, and research on this topic has grown rapidly in recent years. This survey provides a timely review of multi-behavior recommender systems, focusing on three key steps: (1) Data Modeling: representing multi-behaviors at the input level, (2) Encoding: transforming these inputs into vector representations (i.e., embeddings), and (3) Training: optimizing machine-learning models. We systematically categorize existing multi-behavior recommender systems based on the commonalities and differences in their approaches across the above steps. Additionally, we discuss promising future directions for advancing multi-behavior recommender systems.