The aim of optimization algorithm designers is to choose the right algorithm and its proper configuration to solve the problem they face. It is, however, even more important to understand and to be able to explain why this choice is relevant. There is in fact a multitude of algorithms among which it is often difficult to determine which one to use for solving a particular optimization problem — or even a particular problem instance. Indeed, many evolutionary and related search-based optimization algorithms have been proposed for solving a wide range of problems, ranging from single- to multi-objective or continuous to combinatorial optimization. Nevertheless, despite their efficiency and skillful design, it is not always clear in which context an algorithm works best. It is therefore essential to gain a fundamental understanding of their strength and weakness in view of the problem they are aiming to solve. In addition, the informed design and automated selection or configuration of an efficient optimization algorithm is also a challenge that attracts increasing attention from the research community. Landscape analysis is a well-established field that aims to understand the relationship between the underlying structure of a given problem search space and algorithms as well as their underlying components and parameters. Starting by introducing state-of-the-art tools for single-objective landscapes, we identify the key differences and additional properties to address multi-objective landscapes. We expose and contrast the impact of landscape characteristics on the performance of single- and multi-objective optimization algorithms. We identify a sound and concise summary of features characterizing the landscape of a problem instance. We also review the fundamental principles for designing new relevant features, and we show the main methodologies for sampling combinatorial and continuous search spaces. By providing effective tools and practical examples from landscape analysis, further insights are provided on the importance of ruggedness, multimodality and objective correlation in predicting algorithm performance for unseens problems. We conclude with guidelines for the design of search-based optimization by means of key landscape features, and we identify a number of open challenges for the future of landscape analysis and (evolutionary) optimization algorithms.