Satellite remote sensing has become a key technology for monitoring Earth and the processes occurring at its surface. It relies on state-of-the-art machine learning models that require large annotated datasets to capture the extreme diversity of the problems of interest to achieve effective monitoring. While datasets for established problems like land cover classification exist, niche applications such as marine debris detection, deforestation, or glacier dynamics monitoring still miss datasets of sufficient size and variety to train successful deep learning models. Despite some advances in transfer learning, current approaches remain problem-specific and perform poorly out of domain. In this work, we propose METEOR, a meta-learning model providing a holistic, fine-grained classification setup capable of adapting to new problems with limited labels. We demonstrate the performance and versatility of METEOR on a series of remote sensing benchmark tasks from different disciplines.