Who can do this: anyone who can edit the list changes it for that list. Owners, Admins and Contributors set the defaults for new lists.

Candidately can email clients when you add or remove candidates, and remind them about candidates they haven't looked at yet.

The three choices per client

When you share a list, the bell next to each contact sets their emails:

Unsubscribed: no update emails.
Subscribed to list updates: an email when candidates are added or removed.
Subscribed to list updates & Automated follow-ups: the same, plus reminders about candidates they haven't viewed.

Clients can change this themselves with the Subscribed menu on the list.

Set what's sent for a list

Open the list and click List configuration > Client notifications.
Under Default notification preference, choose what new contacts get.
Under Client Subscriptions to Candidate List Updates, turn Notify when a candidate is added to a list and Notify when a candidate is removed from a list on or off.
Under Clients subscribed to automatic follow-up, set when the first reminder goes (for example after 1 day), how often it repeats (every 2 days) and how many more times (3).
Click Save changes.

Settings > Client notifications has the same settings. They apply to lists you create from then on; existing lists keep their own.

Update emails don't go out straight away. Candidately collects changes for about 15 minutes, then sends one email. Activity > Scheduled email notifications shows what's waiting.
Follow-ups only go out for candidates the client hasn't viewed yet.
No follow-ups on weekends. Days are counted in the list owner's time zone.
To stop all emails to one client, set them to Unsubscribed.