Abstract: The conjugacy problem in RAAGs was first solved by Green in the 90s, and has a quick linear time solution provided by Crisp, Godelle and Wiest. This decision problem remains open however for a closely related group, namely virtual RAAGs. In my talk I will introduce the methods used to solve the conjugacy problem in RAAGs, and some of my ideas so far to tackle the conjugacy problem in virtual RAAGs.