You can access new messages by clicking the bell in the top right corner. Messages in a bell are divided into 2 sections:
The first section is dedicated to the current context (course and course group) and shows only new messages from that context. From here you can also access the “All conversations” panel.
Second section shows you new messages from different course groups and different courses. If you are outside of the course context (like Front page or My Courses page), then you will see only the 2nd section.
Each new message notification will be active until you read the full message.