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All of our databases -- including Web of Science, SciFinder, PubMed, Compendex + Inspec -- allow you to save searches and get alerts when new records matching your searches are added to those databases. All offer email alerting options, and most offer RSS feeds.
Since you have to create a user account for SciFinder, you already have the ability to create "Keep Me Posted" alerts.
For the other databases, you'll have to create user accounts to set up email search alerts. To set up RSS feeds, it depends on the database.
Journal Alerts - Tables of Contents and Articles in Press
You can also set up email and/or RSS alerts for individual journals: for the table-of-contents (TOCs) for the latest issues, or more frequent alerting for articles as soon as they are published, which in some cases can be weeks or months before an article is assigned to an issue. Go to the journal website to see what options are available, and whether you need to create a user account to set up the alerting.