Deep neural networks have proven to be very effective for computer vision tasks, such as image classification, object detection, and semantic segmentation -- these are primarily applied to color imagery and video. In recent years, there has been an emergence of deep learning algorithms being applied to hyperspectral and multispectral imagery for remote sensing and biomedicine tasks. These multi-channel images come with their own unique set of challenges that must be addressed for effective image analysis. Challenges include limited ground truth (annotation is expensive and extensive labeling is often not feasible), and high dimensional nature of the data (each pixel is represented by hundreds of spectral bands), despite being presented by a large amount of unlabeled data and the potential to leverage multiple sensors/sources that observe the same scene. In this chapter, we will review recent advances in the community that leverage deep learning for robust hyperspectral image analysis despite these unique challenges -- specifically, we will review unsupervised, semi-supervised and active learning approaches to image analysis, as well as transfer learning approaches for multi-source (e.g. multi-sensor, or multi-temporal) image analysis.