There are notifications inside the site, and I find them, but I find them days later. By the time I read the notification, the conversation has moved on and the question I asked has three replies, two of them answering each other.
The request. An email when somebody replies to a topic you started, and a second one when somebody replies to a reply of yours. The site already sends a weekly newsletter, so the machinery for sending email exists.
What I would want from it. A link, the title of the topic, and the reply. Not the whole thread. The point of the email is to say "there is something here", and the reader decides whether to open it.
What I would want it not to be. A record of every reply to a thread you participated in. That is a firehose, and it is the reason people mute things. I want to be told when the conversation turns to me, not when it continues.
A related request, which may be the same feature. Being able to follow a topic, and to be told when a topic you followed is closed or marked solved. A question of mine gets a reply that solves it, and the person who solved it does not know they solved it, because the topic's author never came back. That is the most useful notification on this site and it does not exist.