Ocean surface monitoring, especially oil slick detection, has become mandatory due to its importance for oil exploration and risk prevention on ecosystems. For years, the detection task has been performed manually by photo-interpreters using Synthetic Aperture Radar (SAR) images with the help of contextual data such as wind. This tedious manual work cannot handle the increasing amount of data collected by the available sensors and thus requires automation. Literature reports conventional and semi-automated detection methods that generally focus either on oil slicks originating from anthropogenic (spills) or natural (seeps) sources on limited data collections. As an extension, this paper presents the automation of offshore oil slicks on an extensive database with both kinds of slicks. It builds upon the slick annotations of specialized photo-interpreters on Sentinel-1 SAR data for 4 years over 3 exploration and monitoring areas worldwide. All the considered SAR images and related annotation relate to real oil slick monitoring scenarios. Further, wind estimation is systematically computed to enrich the data collection. Paper contributions are the following : (i) a performance comparison of two deep learning approaches: semantic segmentation using FC-DenseNet and instance segmentation using Mask-RCNN. (ii) the introduction of meteorological information (wind speed) is deemed valuable for oil slick detection in the performance evaluation. The main results of this study show the effectiveness of slick detection by deep learning approaches, in particular FC-DenseNet, which captures more than 92% of oil instances in our test set. Furthermore, a strong correlation between model performances and contextual information such as slick size and wind speed is demonstrated in the performance evaluation. This work opens perspectives to design models that can fuse SAR and wind information to reduce the false alarm rate.