Computing systems form the backbone of many areas in our society, from manufacturing to traffic control, healthcare, and financial systems. When software plays a vital role in the design, construction, and operation, these systems are referred to as software-intensive systems. Self-adaptation equips a software-intensive system with a feedback loop that either automates tasks that otherwise need to be performed by human operators or deals with uncertain conditions. Such feedback loops have found their way to a variety of practical applications; typical examples are an elastic cloud to adapt computing resources and automated server management to respond quickly to business needs. To gain insight into the motivations for applying self-adaptation in practice, the problems solved using self-adaptation and how these problems are solved, and the difficulties and risks that industry faces in adopting self-adaptation, we performed a large-scale survey. We received 184 valid responses from practitioners spread over 21 countries. Based on the analysis of the survey data, we provide an empirically grounded overview the of state of the practice in the application of self-adaptation. From that, we derive insights for researchers to check their current research with industrial needs, and for practitioners to compare their current practice in applying self-adaptation. These insights also provide opportunities for applying self-adaptation in practice and pave the way for future industry-research collaborations.