After loging in to Cyans, you'll find a left sidebar that lists your topics.
Your topics are sorted into two groups:
Topics in your Inbox need your attention. You can click the topic to read the latest updates, then decide what to do next. Read more about handling your inbox here.
Topics in your Open box are ongoing. You can periodically scan these topics to decide if they need to be followed up (by adding another comment), or closed (if no longer relevant).
Once you close a topic, or you acknowlege a topic that somebody else closed, it is removed from the list. You can always find them back using the search function. To list all topics you've ever participated in, simply search by your username.
If you decide that a closed topic should be reopened, you can simply add a new comment to do so.