We introduce a new video analysis problem -- tracking of rigid planar objects in sequences where both their sides are visible. Such coin-like objects often rotate fast with respect to an arbitrary axis producing unique challenges, such as fast incident light and aspect ratio change and rotational motion blur. Despite being common, neither tracking sequences containing coin-like objects nor suitable algorithm have been published. As a second contribution, we present a novel coin-tracking benchmark containing 17 video sequences annotated with object segmentation masks. Experiments show that the sequences differ significantly from the ones encountered in standard tracking datasets. We propose a baseline coin-tracking method based on convolutional neural network segmentation and explicit pose modeling. Its performance confirms that coin-tracking is an open and challenging problem.