The increasing complexity of microwave and mm-wave devices and components that are required to meet the demands for 5G/6G communication, biomedical, security, and intelligent wireless systems necessitates the development of new methodologies that combine theoretical knowledge with computational power. Classic electromagnetic simulations, although accurate, are computationally intensive. Therefore, their application to high-scale optimization processes is limited. Exploiting machine learning techniques could provide an attractive alternative by providing fast and efficient design of microwave and mm-wave devices and components. Herein, we provide a thorough review of the research efforts made so far on this topic by presenting the current state-of-the-art techniques, methodologies, and systems, including surrogate modeling approaches, inverse design strategies, physics-aware learning schemes, and issues related to model generalization and reproducibility. Additionally, we address specific challenges and issues. Finally, we discuss emerging directions and future trends.