Open Access

The use of surrogate models is a standard method to deal with complex, realworld optimization problems. The first surrogate models were applied to continuous optimization problems. In recent years, surrogate models gained importance for discrete optimization problems. This article, which consists of three parts, takes care of this development. The first part presents a survey of modelbased methods, focusing on continuous optimization. It introduces a taxonomy, which is useful as a guideline for selecting adequate model-based optimization tools. The second part provides details for the case of discrete optimization problems. Here, six strategies for dealing with discrete data structures are introduced. A new approach for combining surrogate information via stacking is proposed in the third part. The implementation of this approach will be available in the open source R package SPOT2. The article concludes with a discussion of recent developments and challenges in both application domains.