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The rapid advancement of computational capabilities has intensified the pursuit of optimal solutions for complex engineering system designs. Traditional brute-force optimization methods are increasingly being replaced by advanced Evolutionary Optimization (EO) methodologies. In recent years, EO techniques have found widespread applications in the design of highly complex engineering systems. Among the various EO approaches, nature-inspired algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and the more recent Brain Storm Optimization (BSO) have gained significant attention. GA enables global exploration of the cost surface through stochastic processes governed by Darwinian evolutionary principles—adaptation, selection, survivability, and mutation. PSO, inspired by the collective intelligence of swarms, models the cooperative behavior of agents (analogous to bees) as they converge toward the most optimal solution using both cognitive and social information. BSO, on the other hand, mimics the collective problem-solving behavior of human brainstorming to achieve efficient global optimization. This Plenary Mater Talk presentation will: (a) provide an engineering-oriented introduction to GA, PSO, and BSO, highlighting their fundamental concepts and recent advances for both new and experienced users; (b) demonstrate the application of these EO techniques to diverse electromagnetic engineering problems, including space and planetary missions, medical and wireless devices, multifunction and adaptive antennas, metamaterials, and nanostructures, (c) assess the advantages and limitations of these optimization techniques in practical engineering contexts and (d) discuss the integration of machine learning techniques and AI platforms to expedite computational processes and enhance optimization efficiency.