Google alerts (news updates)
Great way to get daily or weekly updates on topics you're interested in. These are often news items, but can sometimes be scholarly blogs.
Google Scholar alerts (scholarly publication updates)
Articles from a variety of sources
To create a search alert (when an article about a certain topic is published, you'll get an email): do a search on your topic in Web of Science. Click on the Alerts bell in the left-hand column. Sign in to Web of Science (or register to create a login).
To create a document alert (whenever a particular article is cited by someone else, you'll get an email): find an article. Open it to go to the full record. Click on the Create Citation Alerts bell. Sign in.