For some time now, machine learning methods have been indispensable in many application areas. Especially with the recent development of efficient neural networks, these methods are increasingly used in the sciences to obtain scientific outcomes from observational or simulated data. Besides a high accuracy, a desired goal is to learn explainable models. In order to reach this goal and obtain explanation, knowledge from the respective domain is necessary, which can be integrated into the model or applied post-hoc. We discuss explainable machine learning approaches which are used to tackle common challenges in the bio- and geosciences, such as limited amount of labeled data or the provision of reliable and scientific consistent results. We show that recent advances in machine learning to enhance transparency, interpretability, and explainability are helpful in overcoming these challenges.