Why does Genymotion not connect even after installation?

Last verified against genymotion.com:

If you’re using Genymotion Desktop, ADB should connect automatically to the first running local virtual device. If it still does not, set the proxy with adb shell settings put global http_proxy <ip>:<port> and make sure the Burp certificate is installed correctly. How to connect Burp Suite to Genymotion

For Genymotion SaaS, you must connect the running instance to ADB with gmsaas instances adbconnect <instance_uuid> first, because you cannot use the instance IP directly. How to connect a virtual device to ADB in Genymotion SaaS?