Current developments in natural language processing offer challenges and opportunities for low-resource languages and domains. Deep neural networks are known for requiring large amounts of training data which might not be available in resource-lean scenarios. However, there is also a growing body of works to improve the performance in low-resource settings. Motivated by fundamental changes towards neural models and the currently popular pre-train and fine-tune paradigm, we give an overview of promising approaches for low-resource natural language processing. After a discussion about the definition of low-resource scenarios and the different dimensions of data availability, we then examine methods that enable learning when training data is sparse. This includes mechanisms to create additional labeled data like data augmentation and distant supervision as well as transfer learning settings that reduce the need for target supervision. The survey closes with a brief look into methods suggested in non-NLP machine learning communities, which might be beneficial for NLP in low-resource scenarios