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The outstanding properties of graphene have attracted intense research activities to take advantage of this new material for improving existing electronic applications and inventing new ones. Some of the target applications include digital and RF electronics, advanced sensors, semitransparent electronics, low power switches, solar cells, and battery energy storage. While the lack of bandgap in graphene imposes serious limitations on its application for digital electronics, many RF circuits do not require the existence of a bandgap and can be realized in devices with a low on-off current ratio. In this article, we review the recent progress in using graphene for applications in RF and mixed-signal circuits, arguably one of the most promising fields for future graphene electronics.