Analog integrated circuit design is widely considered a time-consuming task due to the acute dependence of analog performance on the transistors’ and passives’ dimensions. An important research effort has been conducted in the past decade to reduce the front-end design cycles of analog circuits by means of various automation approaches. On the other hand, the significant progress in high-performance computing hardware has made machine learning an attractive and accessible solution for everyone. The objectives of this paper were: (1) to provide a comprehensive overview of the existing state-of-the-art machine learning techniques used in analog circuit sizing and analyze their effectiveness in achieving the desired goals; (2) to point out the remaining open challenges, as well as the most relevant research directions to be explored. Finally, the different analog circuits on which machine learning techniques were applied are also presented and their results discussed from a circuit designer perspective.