Realizing the layouts of analog/mixed-signal (AMS) integrated circuits (ICs) is a complicated task due to the high design flexibility and sensitive circuit performance. Compared with the advancements of digital IC layout automation, analog IC layout design is still heavily manual, which leads to a more time-consuming and error-prone process. In recent years, significant progress has been made in automated analog layout design with emerging of several open-source frameworks. This paper firstly reviews the existing state-of-the art AMS layout synthesis frameworks with focus on the different approaches and their individual challenges. We then present recent research trends and opportunities in the field. Finally, we summaries the paper with open questions and future directions for fully-automating the analog IC layout.