We define and tackle region-of-interest adaptive (RoI-adaptive) acquisition for accelerated MRI. Existing methods for identifying k-space sampling patterns in accelerated MRI are optimized for the quality of the entire image or a general image-wide task. However, MRI is often acquired to image a specific RoI, such as a suspected pathology. We demonstrate that a sampling strategy that serves for a general multi-purpose task is often suboptimal for each individual objective. We propose a framework that efficiently learns MRI sampling masks specific to the RoI, leading to substantially faster acquisition that still enables accurate analysis of the RoI. We show empirically that our RoI-adaptive acquisition approach significantly outperforms general acquisition baselines in the RoI reconstruction and segmentation tasks.