Citation alerts let you know when an article or author you choose is cited by a newly publiohed article. You will be sent an email every time the article or authorthat you choose is cited.
Some databases offer citation alerts. Also, some publisher offer citation alerts, but many limit the alerts to citations only from their journals. (For more information about publisher alerts, see here.) Databases may be found by searching or browsing here.
This list may not be comprehensive, but here are some databases that offer citation and author alerts.