In computer engineering, logic synthesis is a process by which an abstract specification of desired circuit behavior is turned into a design implementation in terms of logic gates. Historically, logic synthesis was tightly related to the physical implementation of the logic gates. Nowadays, pushed by the forecasted end of Moore's law, several emerging technologies (e.g., nanodevices, optical computing, quantum computing) are candidates to either replace or co-exist with the de facto standard CMOS technology. The main consequence of the rising of those emerging technologies is that the logic synthesis has to face new issues and, at the same time, exploits new opportunities. The goal of this paper is thus to present three emerging technologies (Vertical Nanowire Field Effect Transistors, Ferroelectric Transistors, and Memristors), how to use them to implement logic gates, and the main challenges and issues for the logic synthesis.