Machine learning approaches, particularly deep neural networks, are showing tremendous success in finding patterns and relationships in large datasets for prediction and classification, which are typically too complex for humans to grasp directly. In many cases, models are learned for automation as soon as manual analysis and interpretation of the data are too costly. Explainable machine learning, which analyzes the decision-making process of machine learning methods in more detail, is used whenever an explanation of the result is needed in addition to the result. This can be for various reasons, such as increasing trust in the result or deriving new scientific knowledge that can be inferred from patterns in the decision-making process of the machine learning model. In this lecture, we will consider the basics of explainable machine learning, reasons to seek explanations, and some applications and methods from close-range and satellite-based remote sensing. Applications include whale detection, ozone value estimation, and discovery of wilderness characteristics.