Synthetic Aperture Radar (SAR) data and Interferometric SAR (InSAR) products in particular, are one of the largest sources of Earth Observation data. InSAR provides unique information on diverse geophysical processes and geology, and on the geotechnical properties of man-made structures. However, there are only a limited number of applications that exploit the abundance of InSAR data and deep learning methods to extract such knowledge. The main barrier has been the lack of a large curated and annotated InSAR dataset, which would be costly to create and would require an interdisciplinary team of experts experienced on InSAR data interpretation. In this work, we put the effort to create and make available the first of its kind, manually annotated dataset that consists of 19,919 individual Sentinel-1 interferograms acquired over 44 different volcanoes globally, which are split into 216,106 InSAR patches. The annotated dataset is designed to address different computer vision problems, including volcano state classification, semantic segmentation of ground deformation, detection and classification of atmospheric signals in InSAR imagery, interferogram captioning, text to InSAR generation, and InSAR image quality assessment.