Researchers and engineers have increasingly used Deep Learning (DL) for a variety of Remote Sensing (RS) tasks. However, data from local observations or via ground truth is often quite limited for training DL models, especially when these models represent key socio-environmental problems, such as the monitoring of extreme, destructive climate events, biodiversity, and sudden changes in ecosystem states. Such cases, also known as small data problems, pose significant methodological challenges. This review summarises these challenges in the RS domain and the possibility of using emerging DL techniques to overcome them. We show that the small data problem is a common challenge across disciplines and scales that results in poor model generalisability and transferability, yet this has not been investigated in a structured way. We first introduce ten emerging DL techniques: transfer learning, self-supervised learning, semi-supervised learning, few-shot learning, zero-shot learning, active learning, weakly supervised learning, multitask learning, process-aware learning, and ensemble learning; we also include a validation technique known as spatial k-fold cross validation. These techniques have shown promising potential in other scientific disciplines, but have been rarely applied in the RS domain. We also provide guidance on which learning technique to use in various cases, which helps to create a more methodologically robust DL application (and a greater number of them) that can be used to tackle socially important problems with limited data.