Several evolutionary algorithms (EAs) have emerged in recent decades that mimic the behaviour and evolution of biological entities. EAs are widely used to solve single and multi-objective optimization engineering problems. EAs have also been applied to a variety of microwave components, antenna design, radar design, and wireless communications problems. These techniques, among others, include genetic algorithms (GAs), evolution strategies (ES), particle swarm optimization (PSO), differential evolution (DE), and ant colony optimization (ACO). In addition, new innovative algorithms that are not only biology-based but also physics-based or music-based are also emerging, as are hybrid combinations of EAs. The use of evolutionary algorithms is having an increasing impact on antenna design and wireless communications problems. EAs combined with numerical methods in electromagnetics have obtained significant and successful results. This book aims to present some of the emerging Eas and their variants. Chapter 1 introduces the optimization methods in general and the evolutionary algorithms. Chapter 2 presents briefly some of the most popular evolutionary algorithms, such as particle swarm optimization (PSO), differential evolution (DE), and ant colony optimization (ACO) as well as some emerging ones. Chapter 3 focuses on antenna array synthesis, which constitutes a wide range of antenna design problems. Chapter 4 gives an overview of patch antenna design using evolutionary algorithms. Chapter 5 presents design cases from different microwave structure cases. Chapter 6 discusses on various representative design problems in wireless communications. Chapter 7 deals with design cases for 5G and beyond.