ActiveCollab can check IMAP mailbox and import messages. Replies to notifications are imported as comments, and email sent to project address is imported as new tasks (or discussions, when clients send them).
In case that you do not receive replies to notifications, please make sure that check_imap_every_3_minutes cron job is properly configured and running.
Each project has an email address that users can send messages to. System imports these messages as discussions when they are sent by clients who don't have permissions to create tasks, or as tasks for all other known users.
In case messages are not imported, check the following:
Plus addressing is a feature of email server where messages sent to email@example.com get delivered to firstname.lastname@example.org mailbox. This feature has been popularized by Gmail, and people find it useful because it lets them create rules that automatically sort or handle messages that come with a specific value after + sign.
For example, you may subscribe to all newsletters using email@example.com, and set up a rule that automatically movers messages send to that address to a folder where you keep your newsletters that you can then read when you find some time.
Some email servers and mail services, like Microsoft Exchange and Office 365 are known to be slow to adopt this feature. Vote for inclusion of Plus-Addressing in Office 365 here.