The conventional approach to the online management of distributed systems---represented by such standards as SNMP for network management, and WSDM for systems based on service oriented computing (SOC)---relies on the components of the managed system to cooperate in the management process, by providing the managers with the means to monitor their state and activities, and to control their behavior. Unfortunately, the trust thus placed in the cooperation of the managed components is unwarranted for many types of systems---such as systems based on SOA---making the conventional management of such systems unreliable and insecure. This paper introduces a radically new approach to the management of distributed systems, called governance-based management (GBM), which is based on a middleware that can govern the exchange of messages between system components. GBM has a substantial ability to manage distributed systems, in a reliable and secure manner, even without any trustworthy cooperation of the managed components. And it can fully incorporate the conventional management techniques wherever such cooperation can be trusted. GBM also supports a reflexive mode of management, which manages the management process itself, making it safer. However, GBM is still a work in progress, as it raises several open problems that needs to be addressed before this management technique can be put to practice.