Abstract Software and software-controlled technical systems play an increasing role in our daily lives. In cyber-physical systems, which connect the physical and the digital world, software does not only influence how we perceive and interact with our environment but software also makes decisions that influence our behavior. Therefore, the ability of software systems to explain their behavior and decisions will become an important property that will be crucial for their acceptance in our society. We call software systems with this ability explainable software systems. In the past, we have worked on methods and tools to design explainable software systems. In this article, we highlight some of our work on how to design explainable software systems. More specifically, we describe an architectural framework for designing self-explainable software systems, which is based on the MAPE-loop for self-adaptive systems. Afterward, we show that explainability is also important for tools that are used by engineers during the development of software systems. We show examples from the area of requirements engineering where we use techniques from natural language processing and neural networks to help engineers comprehend the complex information structures embedded in system requirements.