<p>Surrogate-based multi-objective optimization has become a cornerstone technique for tackling expensive real-world problems in science and engineering. This survey focuses on surrogate-based algorithms that use the decision-maker’s preference information to guide the search toward the most preferred areas of the Pareto front. Considering such preferences not only facilitates the decision-making process for the user but also helps the analyst to save expensive computational budget. This extended survey provides the first comprehensive overview of both explicit and implicit preference modeling within surrogate-based multi-objective optimization. Explicit preferences refer to information directly provided by the decision maker, such as reference points, weights, or rankings, that can be incorporated into the optimization algorithm. Implicit preferences, in contrast, arise from structural properties of the Pareto front itself, such as knee regions, and can be used to guide the search even when the decision maker cannot articulate preferences. We provide an overview of the state-of-the-art, highlight the most important shortcomings in the literature, and present promising directions for further research.</p>