Analog mixed-signal (AMS) circuit architecture has evolved towards more digital friendly due to technology scaling and demand for higher flexibility/reconfigurability. Meanwhile, the design complexity and cost of AMS circuits has substantially increased due to the necessity of optimizing the circuit sizing, layout, and verification of a complex AMS circuit. On the other hand, machine learning (ML) algorithms have been under exponential growth over the past decade and actively exploited by the electronic design automation (EDA) community. This paper will identify the opportunities and challenges brought about by this trend and overview several emerging AMS design methodologies that are enabled by the recent evolution of AMS circuit architectures and machine learning algorithms. Specifically, we will focus on using neural-network-based surrogate models to expedite the circuit design parameter search and layout iterations. Lastly, we will demonstrate the rapid synthesis of several AMS circuit examples from specification to silicon prototype, with significantly reduced human intervention.