Hi Will. Yes, up top you will see Find threads. When you click on it a small pull down menu appears with:
Your Threads
Threads with your Posts
Unanswered Threads (also a good way to see new threads)
You can also watch threads. There is a Watch button in every thread top right. And then in the top menu click on Watched > Watched Threads.
You can also watch forums by clicking the Watch button in a forum top right. Then click on Watched > Watched Forums.
For watched threads or watched forums you should receive notifications when there are new posts to it. But that depends on how you have set notifications (alerts) in your preferences in your account.